A weighted inequality for potential type operators

TL;DR

This paper proves a new weighted inequality for fractional maximal and convolution operators, connecting weak Lebesgue and Wiener amalgam spaces on non-doubling measure spaces, expanding the understanding of these operators in more general settings.

Contribution

It introduces a weighted inequality for potential type operators on non-doubling measure spaces, extending previous results to broader contexts.

Findings

Established a weighted inequality for fractional maximal operators

Extended inequalities to convolution type operators on non-doubling spaces

Connected weak Lebesgue and Wiener amalgam spaces in this framework

Abstract

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.