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Function spaces related to continuous negative definite functions: $\psi$-Bessel potential spaces

Volume 393 / 2001

Walter Farkas, Niels Jacob, René L. Schilling Dissertationes Mathematicae 393 (2001), 1-62 MSC: Primary 46E35; Secondary 31C25, 35S99, 42B99, 47D07, 47G99, 60J45. DOI: 10.4064/dm393-0-1

Abstract

We introduce and systematically investigate Bessel potential spaces associated with a real-valued continuous negative definite function. These spaces can be regarded as (higher order) $L_p$-variants of translation invariant Dirichlet spaces and in general they are not covered by known scales of function spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the existence of quasi-continuous modifications is shown.

Authors

  • Walter FarkasMathematisches Institut
    Universität München
    Theresienstr. 39
    D-80333 München, Germany
    e-mail
  • Niels JacobDepartment of Mathematics
    University of Wales, Swansea
    Singleton Park
    Swansea SA2 8PP
    United Kingdom
    e-mail
  • René L. SchillingSchool of Mathematical Sciences
    University of Sussex
    Falmer
    Brighton BN1 9QH
    United Kingdom
    e-mail

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