Vector-valued non-homogeneous Tb theorem on metric measure spaces

TL;DR

This paper establishes a general vector-valued non-homogeneous Tb theorem on quasimetric spaces with upper doubling measures, integrating recent techniques to handle both domain and range complexities.

Contribution

It introduces a broad Tb theorem applicable to vector-valued functions on quasimetric spaces with upper doubling measures, merging recent advances in the field.

Findings

Proves a vector-valued non-homogeneous Tb theorem

Extends the theorem to quasimetric spaces with upper doubling measures

Integrates recent techniques for domain and range analysis

Abstract

We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is quite general with respect to both of them.