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Brownian motion characterization of some Besov-Lipschitz spaces on domains

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Abstract

We characterize the Besov-Lipschitz spaces with zero boundary conditions on bounded smooth domains. We prove that the appropriate first and second difference norms are equivalent to the norm given in terms of the transition kernel of the Brownian motion killed upon exit from the domain.

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Authors and Affiliations

  1. Department of Mathematics, Washington University, One Brookings Drive, Campus Box 1146, 63130-4899, St.Louis, MO

    Hrvoje Šikić & Mitchell H. Taibleson

  2. Department of Mathematics, University of Zagreb, BijeniÄŤka 30, 10000, Zagreb, Croatia

    Hrvoje Šikić & Mitchell H. Taibleson

Authors
  1. Hrvoje Šikić
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  2. Mitchell H. Taibleson
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Communicated by Guido Weiss

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Šikić, H., Taibleson, M.H. Brownian motion characterization of some Besov-Lipschitz spaces on domains. J Geom Anal 15, 137–180 (2005). https://doi.org/10.1007/BF02921862

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  • DOI: https://doi.org/10.1007/BF02921862

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