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Sharp weak bounds for Hausdorff operators

Точные слабые оценки для операторов Хаусдорфа

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Abstract

We calculate weak bounds for the Hausdorff operator on Lebesgue spaces. As applications, we obtain sharp weak bounds for some integral operators, such as the fractional Hardy operators and Hilbert operators. We also conclude that the Hausdorff operator is bounded from Hardy spaces to weak Lebesgue spaces.

Резюме

Мы вычисляем постоянные в слабых оценках для оператора Хаусдорфа на пространствах Лебега. В качестве приложения, мы получаем точные постоянные в слабых неравенствах для некоторых интегральных операторов, таких как дробные операторы Харди и операторы Гильберта. Мы также показываем, что оператор Хаусдорфа ограниченно деиствует из пространств Харди в слабые пространства Лебега.

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Authors and Affiliations

  1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, P. R. China

    Guilian Gao

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Fayou Zhao

Authors
  1. Guilian Gao
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  2. Fayou Zhao
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Corresponding author

Correspondence to Fayou Zhao.

Additional information

Supported by the NSF of China (Grant # 11201287, 51505295), RF of HDU (Grant # KYS075614051), CSC (Grant # 201406895019), and the NSF of Zhejiang Province of China (Grant # LY16A010013).

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Gao, G., Zhao, F. Sharp weak bounds for Hausdorff operators. Anal Math 41, 163–173 (2015). https://doi.org/10.1007/s10476-015-0204-4

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  • DOI: https://doi.org/10.1007/s10476-015-0204-4

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