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Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

100%

Saksman E., Soto T.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

98-115

We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.

Intrinsic characterizations of distribution spaces on domains

86%

Rychkov V. S.

Studia Mathematica

1998

tom 127

nr 3

277-298

We give characterizations of Besov and Triebel-Lizorkin spaces $B_{pq}^{s}(Ω)$ and $F_{pq}^s(Ω)$ in smooth domains $Ω ⊂ ℝ^n$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Studia Mathematica

1 Rychkov V. S.

1 Saksman E.

1 Soto T.

1 2017

1 1998

Wyniki wyszukiwania

Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

Intrinsic characterizations of distribution spaces on domains