A Littlewood-Paley type inequality期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

A Littlewood-Paley type inequality

Authors:

Email author" target="_blank">Stevo?Stevi?Email author

Institution:

(1) Matemati ccaron

ki Fakultet, Studentski Trg 16, 11000 Beograd, SERBIA

Abstract:

In this note we prove the following theorem: Let u be a harmonic function in the unit ball $B \subset {\mathbf{R}}^{n}$ and $p \in {\left {\frac{{n - 2}} {{n - 1}},1} \right]}$ . Then there is a constant C = C(p, n) such that

${\mathop {\sup }\limits_{0 \leqslant r < 1} }{\kern 1pt} {\kern 1pt} {\int_S {{\left| {u{\left( {r\zeta } \right)}} \right|}^{p} d\sigma {\left( \zeta \right)} \leqslant C{\left( {{\left| {u{\left( 0 \right)}} \right|}^{p} + {\int_B {{\left| {\nabla u{\left( x \right)}} \right|}^{p} {\left( {1 - {\left| x \right|}} \right)}^{{p - 1}} dV{\left( x \right)}} }} \right)}} }$

Keywords:

:" target="_blank">: Harmonic functions Littlewood-Paley inequality Hardy space maximal function unit ball

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏