Area integrals for Riesz measures on the Siegel upper half space of type II
type: Item
instance of: scholarly article
title: Area integrals for Riesz measures on the Siegel upper half space of type II
zbMATH Open document ID: 0779.32002
author: Hitoshi Arai
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-06-17T00:00:00Z
review text: This paper contains a proof of an important inequality comparing integrals of Riesz measures of subharmonic functions with integrals of their admissible maximal functions on the Siegel upper half-space of type II, which is identified by a coordinate change with \((0,\infty)\times H^ n\), where \(H^ n\) is the Heisenberg group. The inequality is an analogue of one obtained by \textit{T. R. McConnel} [Indiana Univ. Math. J. 33, 289-303 (1984; Zbl 0508.31005)] for the Euclidean upper half-space. The proof depends upon ingenious modification of previous results. Cf. \textit{M. Kaneko} [Tohoku Math. J., II. Ser. 39, 589-596 (1987; Zbl 0653.31003)].
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 31C05
zbMATH DE Number: 203566
zbMATH Keywords: area integrals
zbMATH Keywords: subharmonic functions
zbMATH Keywords: Siegel upper half-space
reviewed by: Edwin J. Akutowicz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227254
OpenAlex ID: W2062315579
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DOI: 10.2748/TMJ/1178227254
description: scientific article; zbMATH DE number 203566