In this paper, we obtain the boundedness of the fractional integral operators, the bilinear fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
Let ∠= -△H^n+ V be the Schrdinger operator on the Heisenberg groups H^n,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estima...Let ∠= -△H^n+ V be the Schrdinger operator on the Heisenberg groups H^n,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠.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 Schr ?dinger operator on Morrey spaces with variable exponent.
Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-t...Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.展开更多
By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator which was defined by Owa, Saigo and Srivastava [1...By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator which was defined by Owa, Saigo and Srivastava [1]. Some interesting further consequences are also considered.展开更多
By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the res...By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.展开更多
In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville ...In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville fractional integral operators. Moreover, the results are interpreted in alternative form.展开更多
In this paper, we prove the boundedness from H1(Rn) to L n/n-α ,∞(Rn) for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2...In this paper, we prove the boundedness from H1(Rn) to L n/n-α ,∞(Rn) for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2, ,l.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 strong t...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
Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator i...Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.展开更多
This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary...This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals.展开更多
In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By u...In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.展开更多
In this paper,we will establish the boundedness of the commutator generated by fractional integral operator and RBMO(μ) function on generalized Morrey space in the non-homogeneous space.
Let T_1 be a singular integral with non-smooth kernel or ± I, let T_2 and T_4 be the linear operators and let T_3= ±I. Denote the Toeplitz type operator by T^b= T_1M^bI_αT_2+T_3I_αM^bT_4,where M^bf=bf, and...Let T_1 be a singular integral with non-smooth kernel or ± I, let T_2 and T_4 be the linear operators and let T_3= ±I. Denote the Toeplitz type operator by T^b= T_1M^bI_αT_2+T_3I_αM^bT_4,where M^bf=bf, and I_α is the fractional integral operator. In this paper, we investigate the boundedness of the operator T^b on the weighted Morrey space when b belongs to the weighted BMO space.展开更多
The object of the present paper is to investigate various argument results of analytic and multivalent functions which are defined by using a certain fractional derivative operator. Some interesting applications are a...The object of the present paper is to investigate various argument results of analytic and multivalent functions which are defined by using a certain fractional derivative operator. Some interesting applications are also considered.展开更多
The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we ded...The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we deduce the existence of solution of an initial value problem of fractional order that be studied only on a bounded interval. The main tools used are Schauder fixed point theorem, measure of weak noncompactness, superposition operator and fractional calculus.展开更多
In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 < p < ∞) to L q and...In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 < p < ∞) to L q and from L p to L n/(n α),∞ with power weight,respectively,where T A 1,A 2 ,α (f)(x)=R n R m 1 (A 1 ;x,y)R m 2 (A 2 ;x,y) | x y | n α +m 1 +m 2 2 (x y) f (y)dy and M A 1,A 2 ,α (f)(x)=sup r>0 1 r n α +m 1 +m 2 2 | x y | <r 2 ∏ i=1 R m i (A i ;x,y)(x y) f (y) | dy,and 0 < α < n, ∈ L s (S n 1) (s ≥ 1) is a homogeneous function of degree zero in R n,A i is a function defined on R n and R m i (A i ;x,y) denotes the m i t h remainder of Taylor series of A i at x about y.More precisely,R m i (A i ;x,y)=A i (x) ∑ | γ | <m i 1 γ ! D γ A i (y)(x y) r,where D γ (A i) ∈ BMO(R n) for | γ |=m i 1(m i > 1),i=1,2.展开更多
基金Supported by the National Natural Science Foundation of China(11271330)
文摘In this paper, we obtain the boundedness of the fractional integral operators, the bilinear fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
文摘Let ∠= -△H^n+ V be the Schrdinger operator on the Heisenberg groups H^n,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠.
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 Schr ?dinger operator on Morrey spaces with variable exponent.
基金Supported Partially by NSF of China (10371087) Education Committee of Anhui Province (2003kj034zd).
文摘Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.
文摘By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator which was defined by Owa, Saigo and Srivastava [1]. Some interesting further consequences are also considered.
文摘By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.
文摘In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville fractional integral operators. Moreover, the results are interpreted in alternative form.
基金Supported in part by the NNSF of China under grant #10771110 and #10471069sponsored by the NSF of Ningbo city under grant #2009A610090
文摘In this paper, we prove the boundedness from H1(Rn) to L n/n-α ,∞(Rn) for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2, ,l.
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Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.
文摘This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals.
基金supported by Natural Science Foundation of China（No.11171220） Support Projects of University of Shanghai for Science and Technology（No.14XPM01）
文摘In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.
基金Supported by the NSF of Education Committee of Anhui Province (KJ2011A138)
文摘In this paper,we will establish the boundedness of the commutator generated by fractional integral operator and RBMO(μ) function on generalized Morrey space in the non-homogeneous space.
文摘Let T_1 be a singular integral with non-smooth kernel or ± I, let T_2 and T_4 be the linear operators and let T_3= ±I. Denote the Toeplitz type operator by T^b= T_1M^bI_αT_2+T_3I_αM^bT_4,where M^bf=bf, and I_α is the fractional integral operator. In this paper, we investigate the boundedness of the operator T^b on the weighted Morrey space when b belongs to the weighted BMO space.
文摘The object of the present paper is to investigate various argument results of analytic and multivalent functions which are defined by using a certain fractional derivative operator. Some interesting applications are also considered.
文摘The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we deduce the existence of solution of an initial value problem of fractional order that be studied only on a bounded interval. The main tools used are Schauder fixed point theorem, measure of weak noncompactness, superposition operator and fractional calculus.
基金Supported in part by the NNSF of China under Grant #10771110 and # 11171306the ZNSF of China under Grant LY12A01024
文摘In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 < p < ∞) to L q and from L p to L n/(n α),∞ with power weight,respectively,where T A 1,A 2 ,α (f)(x)=R n R m 1 (A 1 ;x,y)R m 2 (A 2 ;x,y) | x y | n α +m 1 +m 2 2 (x y) f (y)dy and M A 1,A 2 ,α (f)(x)=sup r>0 1 r n α +m 1 +m 2 2 | x y | <r 2 ∏ i=1 R m i (A i ;x,y)(x y) f (y) | dy,and 0 < α < n, ∈ L s (S n 1) (s ≥ 1) is a homogeneous function of degree zero in R n,A i is a function defined on R n and R m i (A i ;x,y) denotes the m i t h remainder of Taylor series of A i at x about y.More precisely,R m i (A i ;x,y)=A i (x) ∑ | γ | <m i 1 γ ! D γ A i (y)(x y) r,where D γ (A i) ∈ BMO(R n) for | γ |=m i 1(m i > 1),i=1,2.
