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An extension of the Uchiyama theorem and its application to composition operators which preserve BMO

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Abstract

Uchiyama constructed certain extremal BMO functions on Euclidean spaces which show that the John-Nirenberg estimate is in some sense remarkably precise. We extend his result to the case of general subdomains of Euclidean spaces. Also, as an application, we characterize Lebesgue measurable maps between general subdomains of Euclidean spaces which preserve BMO.

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Authors and Affiliations

  1. Department of Mathematics, National Defense Academy, Hashirimizu 1-10-20, 239-8686, Yokosuka, Japan

    Yasuhiro Gotoh

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  1. Yasuhiro Gotoh
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Correspondence to Yasuhiro Gotoh.

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To the memory of Professor Nobuyuki Suita

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Gotoh, Y. An extension of the Uchiyama theorem and its application to composition operators which preserve BMO. J. Anal. Math. 97, 133–167 (2005). https://doi.org/10.1007/BF02807405

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  • DOI: https://doi.org/10.1007/BF02807405

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