SHARP CONSTANTS FOR MULTIVARIATE HAUSDORFF q-INEQUALITIES

被引：9
|
作者：
Fan, Dashan [1 ,2 ]
Zhao, Fayou [3 ]
机构：
[1] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321000, Peoples R China
[3] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2019年 / 106卷 / 02期
基金：
中国国家自然科学基金;
关键词：
sharp constant; multivariate Hausdorff operator; q-inequalities; OPERATORS;
D O I：
10.1017/S1446788718000113
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we focus on the multivariate Hausdorff operator of the form H-Phi(f)(x) = integral((0,+infinity)n) Phi(x(1)/t(1), x(2)/t(2),...,x(n)/t(n))/t(1)t(2)...t(n) f(t(1), t(2), ...,tn)dt, where dt = dt(1) dt(2) ... dt(n) or dt = d(q)t(1) d(q)t(2) ... d(q)t(n) is the discrete measure in q-analysis. The sharp bounds for the multivariate Hausdorff operator on spaces L-p with power weights are calculated, where p is an element of R\{0}.
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页码：274 / 286
页数：13
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