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
In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size condi...In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.展开更多
In this paper, the authors study the boundedness of the operator [μΩ,b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the...In this paper, the authors study the boundedness of the operator [μΩ,b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω ∈ Lipα(Sn-1)(0 <α≤ 1).展开更多
Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO（R^n）. It is proved that μΩ,bis bounded from the Hardy space H^1 （R^n） into the weak L^1（R^n） space.
It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to ...It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to K· α,p q(R n); if α=n(1-1q)+β then μ Ω(f)(x) is boundedness from H K· α,p q(R n) to W K· α,p q(R n).展开更多
In this paper, the authors study the boundedness of the operator μ^bΩ, the commutator generated by a function b ∈Lipβ （R^n） （0 〈β 〈 1） and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.
In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P（ω1;ω2） into Kq^a、p （ω1; ω2）.
In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with r...In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~' if - 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog^+L(S^1).展开更多
Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.展开更多
In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-...In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-1） and some class WFα（S^n-1）, which relates to Grafakos-Stefanov class. Some previous results are extended and improved.展开更多
In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions ...In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.展开更多
In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.
In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and...In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.展开更多
In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
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(12071437)the Natural Science Foundation of Zhejiang Province,China(LQ22A010018)。
文摘In this paper, the multiple parametric Marcinkiewicz integral operators with mixed homogeneity along surfaces are studied. The Lp-mapping properties for such operators are obtained under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction. The main results essentially improve and extend certain previous results.
基金Supported by the National 973 Project (G.19990751) the SEDF (20010027002).
文摘In this paper, the authors study the boundedness of the operator [μΩ,b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω ∈ Lipα(Sn-1)(0 <α≤ 1).
文摘Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO（R^n）. It is proved that μΩ,bis bounded from the Hardy space H^1 （R^n） into the weak L^1（R^n） space.
文摘It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to K· α,p q(R n); if α=n(1-1q)+β then μ Ω(f)(x) is boundedness from H K· α,p q(R n) to W K· α,p q(R n).
基金Supported by the Natural Science Foundation of Xuzhou Normal University (09XLB02)
文摘In this paper, the authors study the boundedness of the operator μ^bΩ, the commutator generated by a function b ∈Lipβ （R^n） （0 〈β 〈 1） and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.
文摘In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P（ω1;ω2） into Kq^a、p （ω1; ω2）.
文摘In this paper, the two-dimensional Marcinkewicz integral introduced by Stein μ(f)(x)=(∫_0~x|∫_(|x-y|≤1) _(|x-y|)^(Ω(x-y))f(y)dy|~2t^(-3)dt)~2 is shown to be of weak type (1,1) and weighted weak type (1,1) with respect to power weight |x|~' if - 1< α< 0, where Ω is homogeneous of degree 0. has mean value 0 and belongs to Llog^+L(S^1).
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
基金partially supported by Grant-in-Aid for Scientific Research(C)(No.23540228),Japan Society for the Promotion of Science
文摘In the present paper, we consider the boundedness of Marcinkiewicz integral operator μΩ,h,Ф along a surface Г = {x = Ф（｜y｜）y/｜y｜）} on the Triebel-Lizorkin space Fq,q^α（R^n ） for Ω belonging to H1 （Sn-1） and some class WFα（S^n-1）, which relates to Grafakos-Stefanov class. Some previous results are extended and improved.
基金Supported by the NSF of China (G10571122) the NFS of Fujian Province of China (Z0511004)
文摘In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.
基金Supported by the National Science Foundation of China (Grants 10901043, 10701064, 10871173, and 10931001)Hangdian Foundation (KYS075608076)
文摘In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.
文摘In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.
基金supported by NSFC (No. 11201003)University NSR Project of Anhui Province (No. KJ2014A087)
文摘In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
基金Supported by NSF of China (10371087)NSF of Anhui Province(07021019)Education Committee of Anhui Province(KJ2007A009)
文摘Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
