The extended Carleson measure and the derivatives of \(L^ p\) functions
type: Item
instance of: scholarly article
title: The extended Carleson measure and the derivatives of \(L^ p\) functions
zbMATH Open document ID: 0802.42018
author: Biyun Yao
published in: Chinese Annals of Mathematics. Series B
publication date: 1992-09-27T00:00:00Z
review text: The author presents a proof of the fact that, for \(p\geq 2\) and \(n\in \mathbb{Z}_ +\), a positive measure \(\mu\) on \(\mathbb{R}^{n+1}_ +\) is \((n+pr)\)-Carleson if and only if \[ \int_{\mathbb{R}^{n+1}_ +} \bigl(|\partial^ r u/\partial y^ r|^ p+ \sum_{1\leq i\leq n} |\partial^ r u/\partial x^ r_ i|^ p\bigr) d\mu\leq C^ p\| f\|^ p_ p, \] \(u\) being the Poisson integral of \(f\).
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 60795
zbMATH Keywords: extended Carleson measure
zbMATH Keywords: Poisson integral
reviewed by: S. V. Kislyakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 60795