Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan...Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.展开更多
The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I...The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.展开更多
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th...This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).展开更多
Objective: To analyze the impact of an integrated extended care model on improving the quality of life of elderly patients with Type 2 Diabetes Mellitus (T2DM). Methods: A total of 176 patients admitted to the hospita...Objective: To analyze the impact of an integrated extended care model on improving the quality of life of elderly patients with Type 2 Diabetes Mellitus (T2DM). Methods: A total of 176 patients admitted to the hospital from March 2015 to February 2018 were selected and randomly assigned to an observation group and a control group, with 88 patients each. The control group implemented conventional nursing interventions, and the observation group carried out an integrated extended-care model. The level of glycemic control, quality of life, and daily medication adherence between both groups were compared. Results: The observation group showed significant improvement in the level of glycemic control, and their fasting blood glucose, 2-hour postprandial blood glucose, and glycated hemoglobin levels were significantly lower as compared with those in the study group (P < 0.05). The quality of life of the patients in the observation group was higher than that of the control group (P < 0.05). The observation group had a higher compliance score (95.48 ± 7.45) than the control group (81.31 ± 8.72) (t = 8.909, P < 0.05). Conclusion: The integrated extended care model allows patients to receive comprehensive and individualized nursing services after discharge, which improves the effect of drug therapy and the quality of life of patients.展开更多
Under the foundation of Cauchy integral formula on certain distinguished boundary for functions with values in universal Clifford algebra, we define the Cauchy type integral with values in a universal Clifford algebra...Under the foundation of Cauchy integral formula on certain distinguished boundary for functions with values in universal Clifford algebra, we define the Cauchy type integral with values in a universal Clifford algebra, obtain its Cauchy principal value and Plemelj formula on certain distinguished boundary.展开更多
In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the f...In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ(R+) for γ 〉 1 and the sphere function ΩεFβ(S^n-1) for someβ 〉 0 which is distinct from HI(Sn-1).展开更多
In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coeffici...In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.展开更多
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa...Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.展开更多
We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the str...We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].展开更多
The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C p...The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C phases.展开更多
In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as ...In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.展开更多
In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauch...In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.展开更多
We classify a generalized coupled singular Emden-Fowler type system +a(t)vn=0,v+b(t)um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integr...We classify a generalized coupled singular Emden-Fowler type system +a(t)vn=0,v+b(t)um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integrals of the various cases which admit Noether point symmetries are then obtained.This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.展开更多
Let D be a bounded domain with piecewise C^(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(φ^V, S^-, S) and Holder continuous density...Let D be a bounded domain with piecewise C^(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(φ^V, S^-, S) and Holder continuous density function φ(ζ), the authors define a solid angular coefficient α(t) at the point t∈δD, prove that there exist the interior and outer limit values Φ^±(t) under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.展开更多
An equivalent definition of fractional integral on spaces of homogeneous type is given. The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.
Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associa...Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.展开更多
In this paper, we obtain unique common fixed point theorems for two mappings satisfying the variable coefficient linear contraction of integral type and the implicit contraction of integral type respectively in metric...In this paper, we obtain unique common fixed point theorems for two mappings satisfying the variable coefficient linear contraction of integral type and the implicit contraction of integral type respectively in metric spaces.展开更多
In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,...In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].展开更多
In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of...In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral equation can contain three arbitrary constants, two arbitrary constants, one constant and may have unique solution. In the case when general solution of integral equation contains arbitrary constants, we stand and investigate different boundary value problems, when conditions are given in singular point. Besides for considered integral equation, the solution found cane represented in generalized power series. Some results obtained in the general model case.展开更多
基金supported by the NSF of Hebei Province(A2022208007)the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)。
文摘Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
基金Supported by National Nature Science Foundation in China(12101564,11971425,11801508)Nature Science Foundation of Zhejiang province(LY22A010013)Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
文摘The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.
文摘This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).
文摘Objective: To analyze the impact of an integrated extended care model on improving the quality of life of elderly patients with Type 2 Diabetes Mellitus (T2DM). Methods: A total of 176 patients admitted to the hospital from March 2015 to February 2018 were selected and randomly assigned to an observation group and a control group, with 88 patients each. The control group implemented conventional nursing interventions, and the observation group carried out an integrated extended-care model. The level of glycemic control, quality of life, and daily medication adherence between both groups were compared. Results: The observation group showed significant improvement in the level of glycemic control, and their fasting blood glucose, 2-hour postprandial blood glucose, and glycated hemoglobin levels were significantly lower as compared with those in the study group (P < 0.05). The quality of life of the patients in the observation group was higher than that of the control group (P < 0.05). The observation group had a higher compliance score (95.48 ± 7.45) than the control group (81.31 ± 8.72) (t = 8.909, P < 0.05). Conclusion: The integrated extended care model allows patients to receive comprehensive and individualized nursing services after discharge, which improves the effect of drug therapy and the quality of life of patients.
基金Supported by the National Natural Science Foundation of China (10471107)
文摘Under the foundation of Cauchy integral formula on certain distinguished boundary for functions with values in universal Clifford algebra, we define the Cauchy type integral with values in a universal Clifford algebra, obtain its Cauchy principal value and Plemelj formula on certain distinguished boundary.
基金supported by the Fundamental Research Funds for the Central Universities(2015QNA43)
文摘In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
基金Supported by the National Natural Science Foundation of China(11071200,11371295)
文摘In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ(R+) for γ 〉 1 and the sphere function ΩεFβ(S^n-1) for someβ 〉 0 which is distinct from HI(Sn-1).
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.
文摘Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.
基金Supported by Fundamental Research Program 2011-2012
文摘We obtain weak type (1, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].
文摘The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C phases.
文摘In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
基金Project supported by NNSF of China(10471107)RFDP of Higher Eduction of China(20060486001)
文摘In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.
文摘We classify a generalized coupled singular Emden-Fowler type system +a(t)vn=0,v+b(t)um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integrals of the various cases which admit Noether point symmetries are then obtained.This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.
文摘Let D be a bounded domain with piecewise C^(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(φ^V, S^-, S) and Holder continuous density function φ(ζ), the authors define a solid angular coefficient α(t) at the point t∈δD, prove that there exist the interior and outer limit values Φ^±(t) under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.
文摘An equivalent definition of fractional integral on spaces of homogeneous type is given. The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.
文摘Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.
文摘In this paper, we obtain unique common fixed point theorems for two mappings satisfying the variable coefficient linear contraction of integral type and the implicit contraction of integral type respectively in metric spaces.
文摘In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].
文摘In this work, we investigate one class of Volterra type integral equation, in model case, when kernels have first order fixed singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral equation can contain three arbitrary constants, two arbitrary constants, one constant and may have unique solution. In the case when general solution of integral equation contains arbitrary constants, we stand and investigate different boundary value problems, when conditions are given in singular point. Besides for considered integral equation, the solution found cane represented in generalized power series. Some results obtained in the general model case.