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Carleson-Type Measures and Kernel Estimates for Potential-Harmonic Weighted Bergman Spaces on the Unit Ball

Nihat Gökhan Göğüş, Sinem Yelda Sönmez

Abstract

In this paper, weighted Bergman spaces on the unit ball in C^n are investigated. A characterization of the Carleson embeddings is established. Pointwise and norm estimates on the reproducing kernel function of weighted Bergman spaces on the unit ball are proved.

Carleson-Type Measures and Kernel Estimates for Potential-Harmonic Weighted Bergman Spaces on the Unit Ball

Abstract

In this paper, weighted Bergman spaces on the unit ball in C^n are investigated. A characterization of the Carleson embeddings is established. Pointwise and norm estimates on the reproducing kernel function of weighted Bergman spaces on the unit ball are proved.
Paper Structure (6 sections, 10 theorems, 114 equations)

This paper contains 6 sections, 10 theorems, 114 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Carleson Measure Characterization
  3. Examples and Counterexamples
  4. Kernel Estimates
  5. Norm Estimate
  6. Pointwise Estimate

Key Result

Lemma 1.1

Rudin Let $n\ge 2$ be an integer, then there are constants $C_1$ and $C_2$ such that for all $z\in \mathbb{B}-\{0\}$ where which is called the (invariant) Green's function of $\mathbb{B}$.

Theorems & Definitions (20)

  • Lemma 1.1
  • Lemma 1.2: KeheZhu
  • Lemma 1.3
  • Proposition 1.4
  • proof
  • Lemma 2.1
  • proof
  • Theorem 2.2
  • proof
  • Example 2.3
  • ...and 10 more