Some inequalities for generalized fractional integral operators on generalized Morrey spaces

Abstract

Abstract. Boundedness of generalized fractional integral operators on generalized Morrey spaces and their related results were shown by many authors. We consider one of their results in a wider framework. Moreover, we show some inequalities for another operator on generalized fractional integrals on generalized Morrey spaces.Mathematics subject classification (2010): Primary 26A33, 42B35; Secondary 42B25.

Multilinear fractional integrals on Morrey spaces

“…Later many authors considered and sharpened this inequality with m = 1. We refer to [16][17][18][19] for related results.…”

On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators

“…There are many papers in the literature dealing with this subject, including the case when the spaces and/or the operators have generalized parameters. We refer to the papers [1,4,7,8,11,15,16,17,19,20,22,24,30,34,35,36,38].…”

Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces

“…In [20], the second and third authors gave an alternative proof based on a variant of the good-λ inequality of Fefferman and Stein introduced in [5]. In [21], the third author gave another simple proof and extended the result to vector-valued functions.…”