In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseu...In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.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.
A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and l...A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.展开更多
In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is ...In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015),it seems to be natural to consider the convolution property as well.Our result will extend the results by Hakim and Sawano(2017)and Hakim et al.(2017).展开更多
基金Supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (Grant No. 19-483)
文摘In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.
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supported by Grant-in-Aid for Scientific Research(C)(Grant No.16K05209)the Japan Society for the Promotion of Science
文摘A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.
基金supported by Grant-in-Aid for Scientific Research(C)(Grant No.16K05209)Japan Society for the Promotion of Science and Department of Mathematics Analysis and the Theory of FunctionsPeoples’Friendship University of Russia。
文摘In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015),it seems to be natural to consider the convolution property as well.Our result will extend the results by Hakim and Sawano(2017)and Hakim et al.(2017).
