Warianty tytułu
Abstrakty
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.
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 60J45: Probabilistic potential theory
- 47D07: Markov semigroups and applications to diffusion processes
- 47G99: None of the above, but in this section
- 42B99: None of the above, but in this section
- 35S99: None of the above, but in this section
- 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
- 31C25: Dirichlet spaces
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
393
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2001
Twórcy
autor
- Mathematisches Institut, Universität München, Theresienstr. 39, D-80333 München, Germany
autor
- Department of Mathematics, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
autor
- School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
Bibliografia
Języki publikacji
EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm393-0-1
Identyfikatory
DOI
10.4064/dm393-0-1
Kolekcja
DML-PL
