ﻻ يوجد ملخص باللغة العربية
In this paper we consider Hankel operators on domains with bounded intrinsic geometry. For these domains we characterize the $L^2$-symbols where the associated Hankel operator is compact (respectively bounded) on the space of square integrable holomorphic functions.
For a non-empty compact set $E$ in a proper subdomain $Omega$ of the complex plane, we denote the diameter of $E$ and the distance from $E$ to the boundary of $Omega$ by $d(E)$ and $d(E,partialOmega),$ respectively. The quantity $d(E)/d(E,partialOmeg
We describe recent work on the Bergman kernel of the (non-smooth) worm domain in several complex variables. An asymptotic expansion is obtained for the Bergman kernel. Mapping properties of the Bergman projection are studied. Irregularity properties
For any real $beta$ let $H^2_beta$ be the Hardy-Sobolev space on the unit disk $D$. $H^2_beta$ is a reproducing kernel Hilbert space and its reproducing kernel is bounded when $beta>1/2$. In this paper, we study composition operators $C_varphi$ on $H
A multiplicative Hankel operator is an operator with matrix representation $M(alpha) = {alpha(nm)}_{n,m=1}^infty$, where $alpha$ is the generating sequence of $M(alpha)$. Let $mathcal{M}$ and $mathcal{M}_0$ denote the spaces of bounded and compact mu
We introduce a family of weighted BMO and VMO spaces for the unit ball and use them to characterize bounded and compact Hankel operators between different Bergman spaces. In particular, we resolve two problems left open by S. Janson in 1988 and R. Wallsten in 1990.