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Some function spaces on spaces of homogeneous type

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Abstract:

We introduce Campanato, Morrey, BMO and Sobolev-type spaces for mappings from a space of homogeneous type into a complete metric space which possess properties comparable to their classical analogues. In particular we show integral characterizations, the validity of the John–Nirenberg theorem, Poincarè and Sobolev inequalities, Sobolev's embedding theorem and estimates on the pointwise behavior of Sobolev-type mappings.

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Authors and Affiliations

  1. Mathematisches Institut der Friedrich-Alexander-Universität Erlangen–Nürnberg, Bismarckstr. 1 1/2, 91054 Erlangen, Germany. e-mail: kronz@mi.uni-erlangen.de, , , , , , DE

    Manfred Kronz

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  1. Manfred Kronz
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Received: 4 December 2000 / Revised version: 5 July 2001

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Kronz, M. Some function spaces on spaces of homogeneous type. manuscripta math. 106, 219–248 (2001). https://doi.org/10.1007/s002290100205

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  • DOI: https://doi.org/10.1007/s002290100205

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