Littlewood-Paley-Stein type square functions based on Laguerre semigroups

TL;DR

This paper studies Littlewood-Paley-Stein square functions derived from Laguerre semigroups, establishing their Calderon-Zygmund operator properties and mapping behaviors in a homogeneous space setting.

Contribution

It demonstrates that Laguerre semigroup-based g-functions are Calderon-Zygmund operators, extending the theory of harmonic analysis to this context.

Findings

Operators are Calderon-Zygmund in the homogeneous space setting

Mapping properties follow from general Calderon-Zygmund theory

Provides a framework for analyzing Laguerre semigroup-related functions

Abstract

We investigate g-functions based on semigroups related to multi-dimensional Laguerre function expansions of convolution type. We prove that these operators can be viewed as Calderon-Zygmund operators in the sense of the underlying space of homogeneous type, hence their mapping properties follow from the general theory.