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Some remarks on extremal problems in weighted Bergman spaces of analytic functions

Romi Shamoyan, Milos Arsenovic

Abstract

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

Some remarks on extremal problems in weighted Bergman spaces of analytic functions

Abstract

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

Paper Structure

This paper contains 3 sections, 10 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Distance problems in $A^p_{\frac{\nu + 2}{p}}(\mathbb C_+)$ spaces
  3. Distance problems in $A^q_s(\Omega)$ spaces

Key Result

Lemma 1

If $f \in A^p_\alpha (\mathbb C_+)$, $0<p<\infty$ and $\alpha > -1$ then where $0 < p \leq 1$, $\beta \geq \frac{2+\alpha}{p} -2$ or $1 \leq p < \infty$, $\beta \geq \frac{1+\alpha}{p}-1$.

Theorems & Definitions (10)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 4
  • Lemma 5
  • Theorem 4
  • Theorem 5