Optimal constants for a class of Hausdorff operators on Lebesgue spaces

doi:10.3868/s140-DDD-023-0015-x

Front. Math. China

2023, Vol. 18

Issue (4) : 277-285 https://doi.org/10.3868/s140-DDD-023-0015-x

RESEARCH　ARTICLE

Optimal constants for a class of Hausdorff operators on Lebesgue spaces

Xiaomei WU(

)

Xingzhi College, Zhejiang Normal University, Jinhua 321004, China

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Abstract

As the extension of classical Hardy operator and Cesàro operator, Hausdorff operator plays an important role in the harmonic analysis, so it is significant to discuss the boundedness of this kind of operator on various function spaces. The article explores the boundedness of a kind of Hausdorff operators on Lebesgue spaces and calculates the optimal constants for the operators to be bounded on such spaces. In addition, the paper also obtains the necessary and sufficient for a kind of multilinear Hausdorff operators to be bounded on Lebesgue spaces and their optimal constants.

Keywords Hausdorff operators multilinear operators Lebesgue spaces optimal constants

Online First Date: 07 December 2023 Issue Date: 12 December 2023

Cite this article:

Xiaomei WU. Optimal constants for a class of Hausdorff operators on Lebesgue spaces[J]. Front. Math. China, 2023, 18(4): 277-285.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0015-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I4/277

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