Adjoint operator of Bergman projection and Besov space $ B_{1}

TL;DR

This paper establishes bounds for the norm of the adjoint of the Bergman projection operator mapping L^1 space onto the Besov space B_1, providing new insights into its operator norm behavior.

Contribution

It derives two-sided bounds for the norm of the adjoint Bergman projection operator acting on L^1 and mapping onto B_1, a novel result in operator theory.

Findings

The norm of the adjoint operator P* is bounded between 2 and 4.

The paper provides explicit bounds for the operator norm of P*.

It advances understanding of the duality and boundedness properties of Bergman projections.

Abstract

The main result of this paper is related to finding two-sided bounds of norm for the adjoint operator $P^{\ast}$ of the Bergman projection $P,$ where $P$ denotes the Bergman projection wich maps $L^{1}(D,d\lambda(z))$ onto the Besov space $B_{1}.$ Here $d\lambda(z)$ is the M\"obius invariant measure ${(1-|z|^2)^{-2}}{dA(z)}$. It is shown that $2\leq\| P^{\ast}\|\leq 4.$