﻿ 关于双线性Hardy算子的两个端点弱型估计 Two Weak Endpoint Estimates on Bilinear Hardy Operators

Pure Mathematics
Vol.07 No.01(2017), Article ID:19583,7 pages
10.12677/PM.2017.71007

Two Weak Endpoint Estimates on Bilinear Hardy Operators

Chunmei Zhang

School of Mathematics & Computer Science, Anhui Normal University, Wuhu Anhui

Received: Jan. 3rd, 2017; accepted: Jan. 19th, 2017; published: Jan. 22nd, 2017

ABSTRACT

By strict calculation, we mainly give the weak estimate for the boundary of the bilinear Hardy operator on the Morrey space and the weighted Lebesgue space, which is a useful supplement to the existing theory.

Keywords:Hardy Operator, Multiple Hardy Operator, Lp Space, Morrey Space

1. 引言和主要结果

Fu Z [20] 等研究了双线性函数的Hardy算子

(1) [20] 设，且。那么，是有界的，且其算子范数为

(2) [20] 设，i = 1, 2,是有界的，且其算子范数为

2. 主要结果的证明

,

，那么，因为，从而

，由可得

Two Weak Endpoint Estimates on Bilinear Hardy Operators[J]. 理论数学, 2017, 07(01): 43-49. http://dx.doi.org/10.12677/PM.2017.71007

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