ﻻ يوجد ملخص باللغة العربية
A class of pseudoconvex domains in $mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the fatness of domains. This range of $p$ is shown to be sharp.
The Bergman theory of domains ${ |{z_{1} |^{gamma}} < |{z_{2}} | < 1 }$ in $mathbb{C}^2$ is studied for certain values of $gamma$, including all positive integers. For such $gamma$, we obtain a closed form expression for the Bergman kernel, $mathbb{B
We obtain sharp ranges of $L^p$-boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating $L^p$-bounde
We completely characterize the boundedness of the area operators from the Bergman spaces $A^p_alpha(mathbb{B}_ n)$ to the Lebesgue spaces $L^q(mathbb{S}_ n)$ for all $0<p,q<infty$. For the case $n=1$, some partial results were previously obtained by
Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $gamma$. A surprising consequence of the analysis is that, whene
This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the failure of Condition R, to deviant boundary behavior of the kernel, and to L^p mapping properties of the kernel.