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$%C. Schneider, On dilation operators in Besov spaces, Rev. Mat. Complut. 22 (2009), no. 1, 111–128.%$
We consider dilation operators in the framework of Besov spaces when . If , is a bounded linear operator from into itself and there are optimal bounds for its norm. We study the situation on the line , an open problem mentioned in "Function spaces, entropy numbers, differential operators" (Edmunds and Triebel, 1996). 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.
Key words: Besov spaces, dilation operators, moment conditions.
2000 Mathematics Subject Classification: 46E35.