On Hardy spaces in complex ellipsoids
type: Item
instance of: scholarly article
title: On Hardy spaces in complex ellipsoids
zbMATH Open document ID: 0944.32004
author: Thomas Hansson
publication date: 1999-11-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75391
review text: Let \(B^p\), \(p=(p_1,\dots,p_n)\), \(p_j\in Z^+\), be a domain with defining function \(\rho(z)= \sum^n_{j=1}|z_j|^{2p_j-1}\). Let \[ Hf (z)= \left({1\over 2\pi i}\right)^n \int_{\partial B^p}{f(\zeta) \partial \rho (\zeta)\wedge \{\bigl(\overline\partial \partial\rho (\zeta)\bigr)^{n-1} \over \bigl( \partial\rho (\zeta),\zeta- z\bigr)^n},\;z\in B^p. \] The author investigates the properties of this operator \(H\) (Theorem 1, 2, 3, 4). In Theorem 5 the factorization of the function from \(H^1(B^p)\) is obtained.
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1355989
zbMATH Keywords: Hardy spaces
zbMATH Keywords: atomic decomposition
zbMATH Keywords: factorization
zbMATH Keywords: complex ellipsoids
reviewed by: P. Z. Agranovich
MaRDI profile type: Publication
OpenAlex ID: W1992661522
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DOI: 10.5802/AIF.1727
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1355989