Vector-Valued Singular Integrals on Locally Doubling Spaces

TL;DR

This paper establishes the boundedness of vector-valued Calderon-Zygmund operators and maximal functions on locally doubling metric measure spaces, extending harmonic analysis tools to more general geometric settings.

Contribution

It introduces new boundedness results for vector-valued singular integrals and maximal functions in the context of locally doubling spaces, broadening the scope of classical harmonic analysis.

Findings

Proved boundedness of Calderon-Zygmund operators in locally doubling spaces.

Established boundedness of the Hardy-Littlewood maximal function in this setting.

Extended harmonic analysis techniques to more general metric measure spaces.

Abstract

We prove vector-valued boundedness of (suitable) Calderon-Zygmund operators and of the (truncated) Hardy-Littlewood maximal function on a connected locally doubling metric measure space.