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The maximal conjugate and Hilbert operators on real Hardy spaces

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We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H1 to L1, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T2 and R2.

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Authors and Affiliations

  1. University of Sydney, Sydney, NSW 2006, Australia

    Gavin Brown

  2. Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Dai Feng

  3. University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, 6720 Szeged, Hungary

    Ferenc Móricz

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  1. Gavin Brown
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  2. Dai Feng
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  3. Ferenc Móricz
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Brown, G., Feng, D. & Móricz, F. The maximal conjugate and Hilbert operators on real Hardy spaces. Acta Math Hung 109, 53–63 (2005). https://doi.org/10.1007/s10474-005-0234-7

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  • DOI: https://doi.org/10.1007/s10474-005-0234-7

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