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Heat kernel and Lipschitz–Besov spaces

  • Alexander Grigor'yan EMAIL logo and Liguang Liu
Published/Copyright: July 2, 2014

Abstract

On a metric measure space (M,ρ,μ) we consider a family of Lipschitz–Besov spaces Λp,qs that is defined only using the metric ρ and measure μ, and a family of Besov spaces Bp,qs that is defined using an auxiliary self-adjoint operator L and the associated heat semigroup. Under certain assumptions about the heat kernel of L, we prove the identity of the two families of the function spaces.

MSC: 35K08; 46E35

Funding source: German Research Council

Award Identifier / Grant number: SFB 701

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11101425

Funding source: Alexander von Humboldt Foundation

The authors would like to thank the referee for her/his careful reading and helpful comments leading to the improvement of the paper.

Received: 2014-2-21
Revised: 2014-4-16
Published Online: 2014-7-2
Published in Print: 2015-11-1

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