On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product L^{p} and weighted L^{p} spaces

TL;DR

This paper establishes new boundedness and weighted estimates for rough multilinear fractional integral and maximal operators on product and weighted L^p spaces, extending previous results to rough kernel cases.

Contribution

It provides the first comprehensive analysis of rough kernel versions of multilinear fractional operators on product and weighted L^p spaces.

Findings

Established product L^p-estimates for rough multilinear fractional integrals.

Derived weighted and two-weighted estimates for these operators.

Proved weak type estimates on product L^p spaces for rough multi-sublinear fractional maximal operators.

Abstract

The aim of this paper is to get the product Lp-estimates, weighted estimates and two-weighted estimates for rough multilinear fractional integral operators and rough multi-sublinear fractional maximal operators, respectively. The author also studies two-weighted weak type estimate on product Lp (Rn) for rough multi-sublinear fractional maximal operators. In fact, this article is the rough kernel versions of [4, 5]' s results.