In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
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
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
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 obtain that b∈ BMO（Rn） if and only if the commutator[b,Iα]is bounded from the Morrey spaces Lp1,λ1Rn×Lp2,λ2Rnto Lq,λ（Rn）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip...In this paper,we obtain that b∈ BMO（Rn） if and only if the commutator[b,Iα]is bounded from the Morrey spaces Lp1,λ1Rn×Lp2,λ2Rnto Lq,λ（Rn）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β（R^n） if and only if the commutator[b,I_α]is bounded from the Morrey spaces Lp1,λ1）Rn×Lp2,λ（Rnto Lq,λRn,for some appropriate indices p,q,λ,μ.展开更多
The object of the present paper is to investigate some mapping properties of subordinations by certain multivalent functions in the open unit disk associated with fractional integral operator.Furthermore,some applicat...The object of the present paper is to investigate some mapping properties of subordinations by certain multivalent functions in the open unit disk associated with fractional integral operator.Furthermore,some applications to the integral operator are also pointed out.展开更多
We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for th...We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the Lp → Lr boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators.展开更多
In this paper, we prove the M^(k)-type sharp maximal function estimates for the Toeplitz type operators associated to the fractional integral and singular integral operator with non-smooth kernel. As an application, w...In this paper, we prove the M^(k)-type sharp maximal function estimates for the Toeplitz type operators associated to the fractional integral and singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of the operators on the Morrey space.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.
By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbo...By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.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
In this paper, a new numerical method for solving fractional differential equations(FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional int...In this paper, a new numerical method for solving fractional differential equations(FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.展开更多
In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth funct...In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.展开更多
We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maxima...We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.展开更多
In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.
The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of subline...The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.展开更多
This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operator...This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operators and fractional integral operators with homogeneous kernels on block-type spaces.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 bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
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.
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 by the National Natural Science Foundation of China(Grant Nos.1126105511661075)
文摘In this paper,we obtain that b∈ BMO（Rn） if and only if the commutator[b,Iα]is bounded from the Morrey spaces Lp1,λ1Rn×Lp2,λ2Rnto Lq,λ（Rn）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β（R^n） if and only if the commutator[b,I_α]is bounded from the Morrey spaces Lp1,λ1）Rn×Lp2,λ（Rnto Lq,λRn,for some appropriate indices p,q,λ,μ.
基金supported by Daegu National University of Education Research grant in 2024.
文摘The object of the present paper is to investigate some mapping properties of subordinations by certain multivalent functions in the open unit disk associated with fractional integral operator.Furthermore,some applications to the integral operator are also pointed out.
基金supported by National Natural Science Foundation of China (Grant Nos.10931001, 10871173)
文摘We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the Lp → Lr boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators.
基金Supported by the National Natural Science Foundation of China (Grant No. 11901126)the Scientific Research Funds of Hunan Provincial Education Department (Grant No. 19B509)。
文摘In this paper, we prove the M^(k)-type sharp maximal function estimates for the Toeplitz type operators associated to the fractional integral and singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of the operators on the Morrey space.
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By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.
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In this paper, a new numerical method for solving fractional differential equations(FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.
文摘In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.
基金Consejo Nacional de Investigaciones Científicas y Técnicas de la República ArgentinaUniversidad Nacional del Litoral
文摘We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.
基金supported financially by Grant-in-Aid for Young Scientists (B) (Grant No. 21740104), Japan Society for the Promotion of Science
文摘In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality.
基金the North China Electric Power University Youth Foundation(No.200611004)the Renmin University of China Science Research Foundation(No.30206104)
文摘The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.
文摘This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operators and fractional integral operators with homogeneous kernels on block-type spaces.
