The boundedness of fractional integral operators in local and global mixed Morrey-type spaces

Abstract

In this paper, we introduce the local and global mixed Morrey-type spaces and show some properties. Besides, we investigate the boundedness of the fractional integral operators \(I_\alpha \) in these spaces. Firstly, we investigate sufficient and necessary conditions in mixed-norm Lebesgue spaces and necessary conditions for boundedness in the local mixed Morrey-type spaces. Then, we prove the boundedness of \(I_{\alpha }\) by Hardy operators’ boundedness in weighted Lebesgue spaces. Furthermore, we obtain the boundedness of \(I_\alpha \) in global mixed Morrey-type spaces and some corollaries.