Resumen de On Dilation Operators in Besov Spaces
We 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.
