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Block Decomposition and Weighted Hausdorff Content

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  16 December 2019

Hiroki Saito ,
Hitoshi Tanaka  and
Toshikazu Watanabe
Hiroki Saito
Affiliation:
College of Science and Technology, Nihon University, Narashinodai 7-24-1, Funabashi City, Chiba, 274-8501, Japan Email: [email protected]
Hitoshi Tanaka
Affiliation:
Research and Support Center on Higher Education for the hearing and Visually Impaired, National University Corporation Tsukuba University of Technology, Kasuga 4-12-7, Tsukuba City, Ibaraki, 305-8521, Japan Email: [email protected]
Toshikazu Watanabe
Affiliation:
College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo, 101-8308, Japan Email: [email protected]
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Abstract

Block decomposition of $L^{p}$ spaces with weighted Hausdorff content is established for $0<p\leqslant 1$ and the Fefferman–Stein type inequalities are shown for fractional integral operators and some variants of maximal operators.

Keywords

block decompositionChoquet integralFefferman–Stein inequalityfractional integral operatorfractional maximal operatorweighted Hausdorff content

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B35: Function spaces arising in harmonic analysis
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 1 , March 2020 , pp. 141 - 156
Copyright
© Canadian Mathematical Society 2019

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Footnotes

Author H. S. is supported by Grant-in-Aid for Young Scientists (19K14577), the Japan Society for the Promotion of Science. Author H. T. is supported by Grant-in-Aid for Scientific Research (C) (15K04918 and 19K03510), the Japan Society for the Promotion of Science.

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