The Haar system in Besov-type spaces
Tom 253 / 2020
Studia Mathematica 253 (2020), 129-162
MSC: Primary 42C15; Secondary 46E35.
DOI: 10.4064/sm180828-9-7
Opublikowany online: 27 January 2020
Streszczenie
Some Besov-type spaces can be characterized in terms of the behavior of the Fourier–Haar coefficients. In this article, the authors discuss some necessary restrictions on the parameters s, \tau , p, q and n in order to have such a characterization. To do so, the authors measure the regularity of the characteristic function \mathcal X of the unit cube in \mathbb {R}^n via Besov-type spaces B^{s,\tau }_{p,q}(\mathbb {R}^n). Furthermore, the authors study necessary and sufficient conditions for the operation \langle f, \mathcal {X} \rangle to generate a continuous linear functional on B^{s,\tau }_{p,q}(\mathbb {R}^n).
