Riesz transforms associated with the twisted Laplacian with drift

TL;DR

This paper investigates the boundedness properties of Riesz transforms of any order linked to the twisted Laplacian with drift on complex space, focusing on their behavior across different L^p spaces.

Contribution

It provides new results on the strong and weak type boundedness of Riesz transforms associated with the twisted Laplacian with drift.

Findings

Proves strong-type (p,p) boundedness for 1<p<∞

Establishes weak-type (1,1) boundedness

Extends understanding of Riesz transforms in complex analysis

Abstract

We consider the Riesz transforms of arbitrary order associated with the twisted Laplacian with drift on $\mathbb{C}^n$ and study their strong-type $(p, p)$, $1<p<\infty$, and weak-type $(1, 1)$ boundedness.