A characterization for the boundedness of positive operators in a filtered measure space

TL;DR

This paper provides a complete characterization of when positive operators are bounded between L^p and L^q spaces in filtered measure spaces, using Sawyer type conditions.

Contribution

It introduces a Sawyer type checking condition that fully characterizes the boundedness of positive operators in filtered measure spaces.

Findings

Complete characterization of bounded positive operators

Introduction of Sawyer type checking condition

Applicable for 1<p≤q<∞

Abstract

In terms of Sawyer type checking condition, a complete characterization is established for which the positive operator in a filtered measure space is bounded from $L^p(d\mu)$ to $L^q(d\mu)$ with $1<p\le q<\infty$.