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Littlewood–Paley theory for Morrey spaces and their preduals

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Abstract

Zorko proved that Morrey spaces are known to have preduals. In the present paper such predual spaces are shown to be characterized by means of the Littlewood–Paley operators. Recently, many function spaces are shown to admit the Littlewood–Paley characterization. As for the predual spaces of Morrey spaces, it had not been clear that a pointwise increasing norm-bounded sequence has a least bound. However, the author proved in the earlier paper that it actually has a least bound. In the present paper, by taking advantage of this property, a characterization by means of Littlewood–Paley operators is proposed.

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Acknowledgments

The second author was supported financially by Grant-in-Aid for Young Scientists (B) No. 24740085, Japan Society for the Promotion of Science. Tanaka was supported by the FMSP program at Graduate School of Mathematical Sciences, the University of Tokyo, and Grant-in-Aid for Scientific Research (C) (No. 23540187), the Japan Society for the Promotion of Science. The authors are grateful to the anonymous referee for his kind suggestion, which made us aware of the difference between two different Littlewood–Paley characterizations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Yamagata University, 1-4-12 Kojirakawamachi, Yamagata, Yamagata, 990-8560, Japan

    Takashi Izumi

  2. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan

    Yoshihiro Sawano

  3. Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, 153-8914, Japan

    Hitoshi Tanaka

Authors
  1. Takashi Izumi
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  2. Yoshihiro Sawano
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  3. Hitoshi Tanaka
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Correspondence to Yoshihiro Sawano.

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Izumi, T., Sawano, Y. & Tanaka, H. Littlewood–Paley theory for Morrey spaces and their preduals. Rev Mat Complut 28, 411–447 (2015). https://doi.org/10.1007/s13163-014-0158-2

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  • DOI: https://doi.org/10.1007/s13163-014-0158-2

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