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On some improved weighted weak type inequalities

Andrei K. Lerner, Kangwei Li, Sheldy Ombrosi, Israel P. Rivera-Ríos

Abstract

In this paper we obtain the sharp quantitative matrix weighted weak type bounds for the Christ--Goldberg maximal operator $M_{W,p}$ in the case $1<p<2$, improving a recent result by Cruz-Uribe and Sweeting. Also, in the scalar setting, we improve a weak type bound obtained in the aforementioned work for Calderón--Zygmund operators.

On some improved weighted weak type inequalities

Abstract

In this paper we obtain the sharp quantitative matrix weighted weak type bounds for the Christ--Goldberg maximal operator in the case , improving a recent result by Cruz-Uribe and Sweeting. Also, in the scalar setting, we improve a weak type bound obtained in the aforementioned work for Calderón--Zygmund operators.
Paper Structure (6 sections, 15 theorems, 149 equations)

This paper contains 6 sections, 15 theorems, 149 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dyadic lattices, sparse families and Calderón--Zygmund operators
  4. Matrix weights
  5. The Christ--Goldberg maximal operator
  6. Calderón--Zygmund operators

Key Result

Theorem A

Let $1\le p<\infty$. Then and the same bound holds for $M_{W,p}$.

Theorems & Definitions (29)

  • Theorem A: CUIMPRR21CUS23
  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • proof
  • Theorem 2.4
  • ...and 19 more