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A Maximal Function Characterization of the Class H p

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Selected Works of Donald L. Burkholder

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Abstract

Let u be harmonic in the upper half-plane and 0<p< ∞. Then u= Re F for some analytic function F of the Hardy class H p if and only if the nontangential maximal function of u is in L p. A general integral inequality between the non-tangential maximal function of u and that of its conjugate function is established.

Received by the editord September 1, 1970.

AMS 1969 subject classifications. Primary 3067, 3110, 6062.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Department of Statistics, Purdue University, West Lafayette, IN, 47907-2068, USA

    Burgess Davis

  2. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Renming Song

Authors
  1. Burgess Davis
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  2. Renming Song
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Correspondence to Burgess Davis .

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Editors and Affiliations

  1. , Department of Mathematics and, Purdue University, N. University Street 150, West Lafayette, 47907-2068, Indiana, USA

    Burgess Davis

  2. , Department of Mathematics, University of Illinois, Urbana, W. Green St. 1409, Urbana, 61801, Illinois, USA

    Renming Song

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Davis, B., Song, R. (2011). A Maximal Function Characterization of the Class H p . In: Davis, B., Song, R. (eds) Selected Works of Donald L. Burkholder. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7245-3_12

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