Democracy functions of wavelet bases in general Lorentz spaces (Q719506)

The motivation behind this paper is the computation of the efficiency of the greedy algorithm in [\textit{V. N. Temlyakov}, Found. Comput. Math. 3, No. 1, 33--107 (2003; Zbl 1039.41012)], for the \(N\)-term wavelet approximation of functions in weighted Lorentz spaces. The efficiency can be quantified by computing the so-called lower and upper democracy functions \(h_\ell\) and \(h_r\), respectively. In this paper, the authors compute \(h_\ell\) and \(h_r\) for the family of weighted Lorentz spaces \(\Lambda_w^q\), where \(w\) is a general weight and \(q\in (0,\infty)\). Examples illustrating the results are also given.