A lower bound for $A_p$ exponents for some weighted weak-type inequalities

TL;DR

This paper establishes a lower bound for the $A_p$ exponents in weighted weak-type inequalities, linking the bounds to unweighted inequality behavior at extreme p-values, with applications to classical operators.

Contribution

It introduces a weak-type version of previous results, providing a new lower bound for $A_p$ exponents based on unweighted inequality limits as p approaches 1 and infinity.

Findings

Provides a lower bound for $A_p$ exponents in weighted weak-type inequalities.

Connects $A_p$ bounds to unweighted inequality behavior at p→1+ and p→∞.

Includes applications to classical operators.

Abstract

We give a weak-type counterpart of the main result in an earlier work of the first author, E. Rela and T. Luque which allows to provide a lower bound for the exponent of the $A_{p}$ constant in terms of the behaviour of the unweighted inequalities when $p\rightarrow\infty$ and when $p\rightarrow1^{+}$. We also provide some applications to classical operators.