منابع مشابه
On dilation operators in Besov spaces
We consider dilation operators Tk : f → f(2·) in the framework of Besov spaces B p,q(R ) when 0 < p ≤ 1. If s > n ` 1 p − 1 ́ , Tk is a bounded linear operator from B p,q(R ) into itself and there are optimal bounds for its norm. We study the situation on the line s = n `
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We consider dilation operators Tk : f → f(2 k ·) in the framework of Triebel-Lizorkin spaces F s p,q(R ). If s > n max ` 1 p − 1, 0 ́ , Tk is a bounded linear operator from F s p,q(R ) into itself and there are optimal bounds for its norm. We study the situation on the line s = n max ` 1 p − 1, 0 ́ , an open problem mentioned in [ET96, 2.3.1]. It turns out that the results shed new light upon the...
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We determine the trace of Besov spaces Bsp,q(R ) and Triebel-Lizorkin spaces Fsp,q(R ) – characterized via atomic decompositions – on hyperplanes R, n > m ∈ N, for parameters 0 < p, q < ∞ and s > 1 p . The limiting case s = 1 p is investigated as well. We generalize these assertions to traces on the boundary Γ = ∂Ω of bounded C domains Ω. Our results remain valid considering the classical space...
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ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 2009
ISSN: 1988-2807,1139-1138
DOI: 10.5209/rev_rema.2009.v22.n1.16324