Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0685.42008
DOI: 10.4171/RMI/66
author: Patrick Ahern
author: Joaquim Bruna
published in: Revista Matemática Iberoamericana
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39353
review text: Summary: We deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of \({\mathbb{C}}^ n\), that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of \(H^ p\) itself involving only complex-tangential derivatives.
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 32H99
zbMATH DE Number: 4122567
zbMATH Keywords: Hardy-Sobolev spaces
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Littlewood-Paley functions
MaRDI profile type: Publication
OpenAlex ID: W2021571565
description: scientific article; zbMATH DE number 4122567