Some <i>q</i>-inequalities for Hausdorff operators

doi:10.1007/s11464-017-0622-7

Front. Math. China

2017, Vol. 12

Issue (4) : 879-889 https://doi.org/10.1007/s11464-017-0622-7

RESEARCH ARTICLE

Some q-inequalities for Hausdorff operators

Jiuhua GUO, Fayou ZHAO(

)

Department of Mathematics, Shanghai University, Shanghai 200444, China

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Abstract

We calculate the sharp bounds for some q-analysis variants of Hausdorff type inequalities of the form $∫ + ∞ 0 (∫ + ∞ 0 ϕ (t) t f x t d q t) p d q x ≤ C ϕ ∫ b 0 f p (t) d q t .$ As applications, we obtain several sharp q-analysis inequalities of the classical positive integral operators, including the Hardy operator and its adjoint operator, the Hilbert operator, and the Hardy-Littlewood-Pólya operator.

Keywords Sharp constant Hausdorff operator Hilbert operator q-inequality

Corresponding Author(s): Fayou ZHAO

Issue Date: 06 July 2017

Cite this article:

Jiuhua GUO,Fayou ZHAO. Some q-inequalities for Hausdorff operators[J]. Front. Math. China, 2017, 12(4): 879-889.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0622-7
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I4/879

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