Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A sufficient condition for $L^p$ regularity of the Berezin transform

Nihat Gokhan Gogus, Sonmez Sahutoglu

Abstract

We prove that the Berezin transform is $L^p$ regular on a large class of domains in $\mathbb{C}^n$ and not $L^2$ regular on the Hartogs triangle.

A sufficient condition for $L^p$ regularity of the Berezin transform

Abstract

We prove that the Berezin transform is regular on a large class of domains in and not regular on the Hartogs triangle.

Paper Structure

This paper contains 3 sections, 8 theorems, 34 equations.

Table of Contents

  1. Proofs of Proposition Prop1 and Theorem Thm1
  2. Proof of Theorem ThmHartogs
  3. Acknowledgement

Key Result

Proposition 1

Let $\Omega$ be a domain in $\mathbb{C}^n$ satisfying property BR and the absolute Bergman projection $P^+_{\Omega}:L^{p_0}(\Omega)\to L^{p_0}(\Omega)$ is bounded for some $1< p_0<\infty$. Then $B_{\Omega}:L^p(\Omega)\to L^p(\Omega)$ is bounded for all $p_0\leq p\leq \infty$ and

Theorems & Definitions (18)

  • Definition 1
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • proof : Proof of Proposition \ref{['Prop1']}
  • Remark 1
  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • ...and 8 more