Hankel Bilinear forms on generalized Fock-Sobolev spaces on ${\mathbb C}^n$

Autor:	Cascante, Carme, Fàbrega, Joan, Pascuas, Daniel
Rok vydání:	2019
Předmět:	Mathematics - Complex Variables Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock-Sobolev spaces on ${\mathbb C}^n$ with respect to the weight $(1+|z|)^\rho e^{-\frac{\alpha}2|z|^{2\ell}}$, for $\ell\ge 1$, $\alpha>0$ and $\rho\in{\mathbb R}$. We obtain a weak decomposition of the Bergman kernel with estimates and a Littlewood-Paley formula, which are key ingredients in the proof of our main results. As an application, we characterize the boundedness, compactness and the membership in the Schatten class of small Hankel operators on these spaces. Comment: Accepted for publication in Annales Academiae Scientiarum Fennicae Mathematica
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1912.09241 Zobrazit plný text záznamu View this record from Arxiv