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Littlewood–Paley Equivalence and Homogeneous Fourier Multipliers

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Abstract

We consider certain Littlewood–Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for Hörmander’s theorem on the invertibility of homogeneous Fourier multipliers. Also, applications to the theory of Sobolev spaces will be given.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Kanazawa University, Kanazawa, 920-1192, Japan

    Shuichi Sato 

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  1. Shuichi Sato 
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Correspondence to Shuichi Sato .

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The author is partly supported by Grant-in-Aid for Scientific Research (C) No. 25400130, Japan Society for the Promotion of Science.

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Sato , S. Littlewood–Paley Equivalence and Homogeneous Fourier Multipliers. Integr. Equ. Oper. Theory 87, 15–44 (2017). https://doi.org/10.1007/s00020-016-2333-y

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  • DOI: https://doi.org/10.1007/s00020-016-2333-y

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