On the behaviors of rough fractional type sublinear operators on vanishing generalized weighted Morrey spaces

TL;DR

This paper investigates the boundedness of rough fractional type sublinear operators on vanishing generalized weighted Morrey spaces, providing conditions under which these operators are bounded, with applications to harmonic analysis.

Contribution

It establishes new boundedness results for rough fractional integral and maximal operators on vanishing generalized weighted Morrey spaces, extending harmonic analysis tools.

Findings

Boundedness of rough sublinear operators on vanishing generalized weighted Morrey spaces.

Conditions satisfied by most operators in harmonic analysis.

Examples include rough fractional integral and maximal operators.

Abstract

The aim of this paper is to get the boundedness of rough sublinear operators generated by fractional integral operators on vanishing generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. Also, rough fractional integral operator and a related rough fractional maximal operator which satisfy the conditions of our main result can be considered as some examples.