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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.

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