Carleson inequalities in classes of derivatives of harmonic Bergman functions with \(0<p\leq 1\)
type: Item
instance of: scholarly article
title: Carleson inequalities in classes of derivatives of harmonic Bergman functions with \(0<p\leq 1\)
zbMATH Open document ID: 0938.46030
author: Masahiro Yamada
published in: Hiroshima Mathematical Journal
publication date: 2000-06-27T00:00:00Z
review text: The author studies conditions on a \(\sigma\)-finite positive Borel measure \(\mu\), for the inequality \[ \Biggl(\int|D^\alpha u|^q d\mu\Biggr)^{1/q}\leq C\Biggl(\int|D^m_y u|^p y^r dV\Biggr)^{1/p} \] to be true (and in particularly \(\int|u|^p d\mu\leq C\int|D_y u|^p y^r dV\), where \(p\leq 1\), \(u\) belongs to the Bergman space \(b^p\)). Part 3 contains a necessary and sufficient condition for \(\mu\) on the upper half space to satisfy the considered inequality. In Part 4, the author shows that when \(p\leq 1\) the Bergman norm is comparable to several derivative norms. The paper is very interesting and contains several very important lemmas and theorems with long and full proofs.
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1310264
zbMATH Keywords: Carleson inequalities
zbMATH Keywords: classes of derivatives of harmonic Bergman functions
reviewed by: Aleksander Waszak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206125159
OpenAlex ID: W1984534740
DOI: 10.32917/HMJ/1206125159
description: scientific article; zbMATH DE number 1310264