Limiting weak-type behaviors of some integral operators

TL;DR

This paper investigates the limiting weak-type behaviors of various integral operators, providing optimal results that enhance and extend existing theoretical understanding in harmonic analysis.

Contribution

It introduces new optimal limiting weak-type bounds for several integral operators, advancing the theoretical framework beyond prior results.

Findings

Established new limiting weak-type bounds for maximal and singular integral operators.

Extended previous results to include fractional and truncated singular integrals.

Improved the understanding of the asymptotic behaviors of these operators.

Abstract

In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type behaviors are given, which essentially improve and extend the previous results in this topics.