Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel) | Zendy

Niels Jacob | Zendy; René L. Schilling | Zendy

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Function Spaces as Dirichlet Spaces (About a Paper by Maz'ya and Nagel)

Author(s) -

Niels Jacob,

René L. Schilling

Publication year - 2005

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1228

Subject(s) - mathematics , dirichlet distribution , function (biology) , pure mathematics , function space , mathematical analysis , biology , evolutionary biology , boundary value problem

V. G. Maz'ya and J. Nagel found for certain classes of weighted Sobolev norms (defined using the Fourier transform) equivalent Slobodeckij-type dierence representations. We extend these considerations to a wider class of anisotropic norms which arise in the theory of Markov processes. In particular we show that these Sobolev norms are equivalent to Dirichlet norms.

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