Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$

Details Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$ Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$

2010-04-05

arxiv.org/abs/1004.0720v3

J. Math. Anal. Appl. 371 (2010), 341-346

Mathematics

Functional Analysis

9 pages. Fixed some typos, to appear in J. Math. Anal. Appl

Scientific paper

Let $\mathbb{D}^n$ be the polydisk in $\mathbb{C}^n$ and the symbols $\phi,\psi\in C(\bar{\mathbb{D}^n})$ such that $\phi$ and $\psi$ are pluriharmonic on any $(n-1)$-dimensional polydisk in the boundary of $\mathbb{D}^{n}.$ Then $H^*_{\psi}H_{\phi}$ is compact on $A^2(\mathbb{D}^n)$ if and only if for every $1\leq j,k\leq n$ such that $j\neq k$ and any $(n-1)$-dimensional polydisk $D$, orthogonal to the $z_j$-axis in the boundary of $\mathbb{D}^n,$ either $\phi$ or $\psi$ is holomorphic in $z_k$ on $D.$ Furthermore, we prove a different sufficient condition for compactnes of the products of Hankel operators. In $\mathbb{C}^2,$ our techniques can be used to get a necessary condition on some product domains involving annuli.

Affiliated with

Also associated with

No associations

Rating

Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-56605