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}.
引用
收藏
页码：274 / 286
页数：13
相关论文
共 19 条
  • [1] Taylor-Widder representation formulae and Ostrowski, Gruss, integral means and Csiszar type inequalities
    Anastassiou, George A.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (01) : 9 - 23
  • [2] q-Fractional Calculus and Equations Preface
    Ismail, Mourad
    [J]. Q-FRACTIONAL CALCULUS AND EQUATIONS, 2012, 2056 : IX - +
  • [3] [Anonymous], AN STIINT AL I CU 1A
  • [4] SOME NEW HARDY TYPE INEQUALITIES IN q-ANALYSIS
    Baiarystanov, A. O.
    Persson, L. E.
    Shaimardan, S.
    Temirkhanova, A.
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2016, 10 (03): : 761 - 781
  • [5] Variational calculus on q-nonuniform lattices
    Bangerezako, G
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 306 (01) : 161 - 179
  • [6] Hausdorff operators on Euclidean spaces
    Chen Jie-cheng
    Fan Da-shan
    Wang Si-lei
    [J]. APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2013, 28 (04) : 548 - 564
  • [7] Ernst T., 2012, A Comprehensive treatment of -calculus
  • [8] Exton H., 1983, ELLIS HORWOOD SERIES
  • [9] Some q-inequalities for Hausdorff operators
    Guo, Jiuhua
    Zhao, Fayou
    [J]. FRONTIERS OF MATHEMATICS IN CHINA, 2017, 12 (04) : 879 - 889
  • [10] Jackson F. H., 1910, Quart. J. Pure Appl. Math., V41, P193, DOI DOI 10.1017/S0080456800002751
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