Two weight norm inequalities for vector-valued operators

TL;DR

This paper investigates two weight norm inequalities for vector-valued operators, establishing conditions for boundedness from weighted L^p spaces to mixed norm spaces, with applications to Wolff's potentials.

Contribution

It provides new characterizations of two weight inequalities for vector-valued operators and applies these to analyze Wolff's potentials.

Findings

Established necessary and sufficient conditions for two weight inequalities

Derived bounds for vector-valued operators in mixed norm spaces

Applied results to demonstrate boundedness of Wolff's potentials

Abstract

We study two weight norm inequalities for a vector-valued operator from a weighted $L^p(\sigma)$-space to mixed norm $L^q_{l^s}(\mu)$ spaces, $1<q<p$. We apply these results to the boundedness of Wolff's potentials.