On Dilation Operators in Besov Spaces
2009; Springer Science+Business Media; Volume: 22; Issue: 1 Linguagem: Inglês
10.5209/rev_rema.2009.v22.n1.16324
ISSN1988-2807
Autores Tópico(s)Advanced Mathematical Physics Problems
ResumoWe consider dilation operators Tk : f → f(2k.) in the framework of Besov spaces Bsp,q (Rn) when 0 < p≤ 1. If s > n(1/p — 1) Tk is a bounded linear operator from Bsp,q (Rn) into itself and there are optimal bounds for its norm. We study the situation on the line s = n(1/p — 1), an open problem mentioned in [5, 2.3.1, 2.3.2]. It turns out that the results shed new light upon the diversity of different approaches to Besov spaces on this line, associated to definitions by differences, Fourier-analytical methods, and subatomic decompositions.
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