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Higher Order Fractional Leibniz Rule

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Abstract

The fractional Leibniz rule is generalized by the Coifman–Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.

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Acknowledgements

The first author was partly supported by the Japan Society for the Promotion of Science, Grant-in-Aid for JSPS Fellows No 26\(\cdot \)7371 and Top Global University Project of Waseda University. The second author was supported in part by INDAM, GNAMPA - Gruppo Nazionale per l’Analisi Matematica, la Probabilita e le loro Applicazion, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and by Top Global University Project, Waseda University. The third author was supported by Grant-in-Aid for Scientific Research (A) Number 26247014.

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Authors and Affiliations

  1. Department of Pure and Applied Physics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kazumasa Fujiwara

  2. Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Vladimir Georgiev

  3. Faculty of Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Vladimir Georgiev

  4. Department of Applied Physics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Tohru Ozawa

Authors
  1. Kazumasa Fujiwara
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  2. Vladimir Georgiev
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  3. Tohru Ozawa
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Corresponding author

Correspondence to Kazumasa Fujiwara.

Additional information

Communicated by Loukas Grafakos.

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Fujiwara, K., Georgiev, V. & Ozawa, T. Higher Order Fractional Leibniz Rule. J Fourier Anal Appl 24, 650–665 (2018). https://doi.org/10.1007/s00041-017-9541-y

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  • DOI: https://doi.org/10.1007/s00041-017-9541-y

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