The Haar system in Besov-type spaces

Some Besov-type spaces B-p,q(s,tau)(R-n) 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 X of the unit cube in R-n via Besov-type spaces B-p,q(s,tau)(R-n). Furthermore, the authors study necessary and sufficient conditions for the operation < f,X > to generate a continuous linear functional on B-p,q(s,tau)(R-n).