# Sharp $A_1$ weighted estimates for vector valued operators

## TL;DR

This paper establishes sharp weighted estimates for vector valued operators like maximal functions and Calderón-Zygmund operators using Aq weights, introducing new convex body domination techniques and a novel proof for scalar cases.

## Contribution

It provides the first sharp weighted bounds for vector valued operators and develops convex body domination results, including a new proof for scalar operators.

## Key findings

- Quantitative weighted L^p estimates for vector valued operators.
- Convex body domination results for singular integrals.
- New proof for scalar weighted estimates.

## Abstract

Given $1\leq q<p<\infty$ quantitative weighted L^p estimates, in terms of Aq weights, for vector valued maximal functions, Calder\'on-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular operators will rely upon suitable convex body domination results, which in the case of commutators will be provided in this work, obtaining as a byproduct a new proof for the scalar case as well.