On Dilation Operators in Besov Spaces

• Autores: Cornelia Schneider
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 22, Nº 1, 2009, págs. 111-128
• Idioma: inglés
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• Resumen

  • 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.