Revisiting Riesz transforms for Hermite and Special Hermite Operators

TL;DR

This paper establishes weighted mixed norm estimates for Riesz transforms linked to Hermite and special Hermite operators, connecting these estimates to vector-valued bounds involving Laguerre functions.

Contribution

It introduces new weighted mixed norm estimates for Riesz transforms of Hermite and special Hermite operators, relating them to vector-valued estimates with Laguerre functions.

Findings

Weighted mixed norm estimates are proven for Riesz transforms.

Estimates are shown to be equivalent to vector-valued estimates for Laguerre function-based operators.

The results extend understanding of Riesz transforms in harmonic analysis.

Abstract

In this paper we prove weighted mixed norm estimates for Riesz transforms associated to Hermite and special Hermite operators. The estimates are shown to be equivalent to vectorvalued esimates for a sequence of operators defined in terms of Laguerre functions of different type.