Abstract
In this paper, we consider some norm estimates for mixed Morrey spaces considered by the first author. Mixed Lebesgue spaces are realized as a special case of mixed Morrey spaces. What is new in this paper is a new norm estimate for mixed Morrey spaces that is applicable to mixed Lebesgue spaces as well. An example shows that the condition on parameters is optimal. As an application, the Olsen inequality adapted to mixed Morrey spaces can be obtained.
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Acknowledgements
Toru Nogayama and Takahiro Ono were supported financially by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists (20J10403 and 20J20606). Daniel Salim was supported by P3MI-ITB Program 2017. Yoshihiro Sawano was supported by Grant-in-Aid for Scientific Research (C) (19K03546), the Japan Society for the Promotion of Science and People’s Friendship University of Russia. The authors are thankful to Dr. Naoya Hatano for pointing out the mistake in the proof of Theorem 4.
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Nogayama, T., Ono, T., Salim, D. et al. Atomic Decomposition for Mixed Morrey Spaces. J Geom Anal 31, 9338–9365 (2021). https://doi.org/10.1007/s12220-020-00513-z
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DOI: https://doi.org/10.1007/s12220-020-00513-z