This paper concerns with the fractional integrals, which are also known as the Riesz potentials. A characterization for the boundedness of the fractional integral operators on generalized Morrey spaces will be present...This paper concerns with the fractional integrals, which are also known as the Riesz potentials. A characterization for the boundedness of the fractional integral operators on generalized Morrey spaces will be presented. Our results can be viewed as a refinement of Nakai＇s.展开更多
In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the...In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) i...The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn...Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.展开更多
Let μ be a Borel measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（Q） ≤ col（Q）^n for any cube Q belong to R^d with sides parallel to the coordinate axes and for some fixed ...Let μ be a Borel measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（Q） ≤ col（Q）^n for any cube Q belong to R^d with sides parallel to the coordinate axes and for some fixed n with 0 〈 n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H^1（μ）.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L es...Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.展开更多
Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα...Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.展开更多
By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.
Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results an...Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos[2].展开更多
In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our...In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.展开更多
In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integ...In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integrals of some functions. The consideration of q-exponential function in that sense leads to q-analogs of Mittag-Leffier function.展开更多
Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)...Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)belongs to the Orlicz space Osc_(exp L^(si)).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.
We prove the boundedness of fractional integral with a rough kernel on Triebel-Lizorkin spaces, where the rough kernel belongs to the block space and does not need to satisfy any moment conditions on the unit sphere.
In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagran...In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.展开更多
Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Mor...Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with it, which, in the case when μ is the d-dimensional Lebesgue measure, also improve the known results.展开更多
文摘This paper concerns with the fractional integrals, which are also known as the Riesz potentials. A characterization for the boundedness of the fractional integral operators on generalized Morrey spaces will be presented. Our results can be viewed as a refinement of Nakai＇s.
文摘In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
基金Supported by the973Project( G1 9990 75 1 0 5 ) and the National Natural Science Foundation of China( 1 0 2 71 0 1 6)
文摘The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.
文摘Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.
文摘Let μ be a Borel measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（Q） ≤ col（Q）^n for any cube Q belong to R^d with sides parallel to the coordinate axes and for some fixed n with 0 〈 n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H^1（μ）.
基金The Science and Technology Research(Z2014057)of Higher Education in Hebei Provincethe Doctoral Foundation(L2015B05)of Hebei Normal Universitythe NSF(A2015403040)of Hebei Province
文摘Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.
文摘Suppose b= （b1,…,bm） E （BMO）^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights.
基金The NSF(11561057,11226104)of Chinathe NSF(20151BAB211002,20151BAB201007)of Jiangxi Province+1 种基金the Science Foundation(GJJ151054,GJJ151061)of Jiangxi Education Departmentthe Scientific Research Project of Shangrao Normal University
文摘By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.
文摘Shi and Wao[6] studied the boundedness of multilinear fractional integrals introduced by Kenig and Stein[3] on product of weighted LP-spaces, and got some results. We give some remarks with respect to their results and correct some mistakes. We also consider another multilinear fractional integral introduced by Grafakos[2].
基金Supported by RFDP of China (Grant No. 20050027025)NSF of China (Grant No. 10571014, 10571015)
文摘In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.
基金Supported by Ministry of Science,Technology and Development of Republic Serbia (Grant Nos.144023 and 144013)
文摘In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integrals of some functions. The consideration of q-exponential function in that sense leads to q-analogs of Mittag-Leffier function.
文摘Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)belongs to the Orlicz space Osc_(exp L^(si)).
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This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11561057, 11471309, 11271175） and the Natural Science Foundation of Jiangxi Province （No 20151BAB211002）.
文摘We prove the boundedness of fractional integral with a rough kernel on Triebel-Lizorkin spaces, where the rough kernel belongs to the block space and does not need to satisfy any moment conditions on the unit sphere.
基金Project supported by the National Natural Science Foundations of China(Grant Nos.11272287 and 11472247)the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)(Grant No.IRT13097)
文摘In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.
基金Supported by the National Natural Science Foundation of China(No.10871025)
文摘Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with it, which, in the case when μ is the d-dimensional Lebesgue measure, also improve the known results.
