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A localization property for B p q s and F p q s spaces

Hans Triebel — 1994

Studia Mathematica

Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

Sobolev-Besov spaces of measurable functions

Hans Triebel — 2010

Studia Mathematica

The paper deals with spaces L p s ( ) of Sobolev type where s > 0, 0 < p ≤ ∞, and their relations to corresponding spaces B p , q s ( ) of Besov type where s > 0, 0 < p ≤ ∞, 0 < q ≤ ∞, in terms of embedding and real interpolation.

Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.

Hans Triebel — 2002

Revista Matemática Complutense

Function spaces of type B and F cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Hölder-Zygmund spaces and inhomogeneous Hardy spaces. In the last 2 or 3 decades they haven been studied preferably on R and in smooth bounded domains in R including numerous applications to pseudodifferential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in...

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