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Closures of Harmonic Bergman Besov Spaces in the Weighted Harmonic Bloch Spaces on the Unit Ball

Ömer Faruk Doğan

Abstract

In this paper, via invertible radial differential operators, we characterize the closures of the harmonic Bergman Besov Spaces in the weighted harmonic Bloch spaces on the unit ball of Rn in terms of natural level sets. To this end, we first show that the harmonic Bergman Besov space is contained in the weighted harmonic little Bloch space.

Closures of Harmonic Bergman Besov Spaces in the Weighted Harmonic Bloch Spaces on the Unit Ball

Abstract

In this paper, via invertible radial differential operators, we characterize the closures of the harmonic Bergman Besov Spaces in the weighted harmonic Bloch spaces on the unit ball of Rn in terms of natural level sets. To this end, we first show that the harmonic Bergman Besov space is contained in the weighted harmonic little Bloch space.
Paper Structure (5 sections, 13 theorems, 51 equations)

This paper contains 5 sections, 13 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. PRELIMINARIES
  3. Main Tools
  4. Proof of Theorem \ref{['Theorem-A']}
  5. Proof of Theorems \ref{['Theorem-1']} and \ref{['Theorem-2']}

Key Result

Theorem 1.1

Let $\alpha \in \mathbb{R}$ and $0<p<\infty$. Then the harmonic Bergman–Besov space $b^p_{p\alpha-n}$ is contained in the weighted harmonic little Bloch space $b^\infty_{\alpha 0}$.

Theorems & Definitions (20)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Definition 2.1
  • Definition 2.2
  • Lemma 2.3
  • Lemma 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Theorem 3.4
  • ...and 10 more