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Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces

100%

Farkas W., Jacob N., Schilling R.

Instytut Matematyczny Polskiej Akademii Nauk

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.

Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains

71%

Cioica P., Dahlke S., Kinzel S., Lindner F., Raasch T., Ritter K., Schilling R.

Studia Mathematica

2011

tom 207

nr 3

197-234

We use the scale of Besov spaces $B^{α}_{τ,τ}(𝓞)$, 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains 𝓞 ⊂ ℝ. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.

Ograniczanie wyników

1 Studia Mathematica

2 Schilling R.

1 Cioica P.

1 Dahlke S.

1 Farkas W.

1 Jacob N.

1 Kinzel S.

1 Lindner F.

1 Raasch T.

1 Ritter K.

1 2011

1 2001

Wyniki wyszukiwania

Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces

Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains