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Heat kernel characterisation of Besov-Lipschitz spaces on metric measure spaces

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Abstract

We give a heat-kernel characterisation of the Besov-Lipschitz spaces Lip (α, p, q)(X) on domains which support a Markovian kernel with appropriate exponential bounds. This extends former results of Grigor’yan et al. (Trans Am Math Soc 355:2065–2095, 2008), Hu and Zähle (Studia Math 170:259–281, 2005), Pietruska-Pałuba (Stoch Stoch Rep 67:267–285, 1999; 70:153–164, 2000), which were valid for \({\alpha = \frac{d_w}{2}, p = 2, q = \infty}\), where d w is the walk dimension of the space X.

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Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Katarzyna Pietruska-Pałuba

  2. Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956, Warsaw, Poland

    Katarzyna Pietruska-Pałuba

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  1. Katarzyna Pietruska-Pałuba
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Correspondence to Katarzyna Pietruska-Pałuba.

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Supported by the KBN grant no. 1-PO3A-008-29

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Pietruska-Pałuba, K. Heat kernel characterisation of Besov-Lipschitz spaces on metric measure spaces. manuscripta math. 131, 199–214 (2010). https://doi.org/10.1007/s00229-009-0310-3

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  • DOI: https://doi.org/10.1007/s00229-009-0310-3

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