On good-$\lambda$ inequalities for couples of measurable functions

TL;DR

This paper establishes a domination condition that implies good-$\lambda$ and exponential inequalities for pairs of measurable functions, leading to new and classical estimates in harmonic analysis, including a novel exponential estimate for Carleson operators.

Contribution

It introduces a general domination condition that yields good-$\lambda$ and exponential inequalities applicable to harmonic analysis operators in abstract measure spaces.

Findings

Derived a new exponential estimate for Carleson operators

Unified classical and new inequalities under a general domination condition

Extended results to abstract measure spaces with a ball-basis

Abstract

We give a domination condition implying good-$\lambda$ and exponential inequalities for couples of measurable functions. Those inequalities recover several classical and new estimations involving some operators in Harminic Analysis. Among other corollaries we prove a new exponential estimate for Carleson operators. The main results of the paper are considered in a general setting, namely, on abstract measure spaces equipped with a ball-basis.