Wavelet bases in generalized Besov spaces

Abstract

In this paper we obtain a wavelet representation in (inhomogeneous) Besov spaces of generalized smoothness via interpolation techniques. As consequence, we show that compactly supported wavelets of Daubechies type provide an unconditional Schauder basis in these spaces when the integrability parameters are finite.  2004 Elsevier Inc. All rights reserved.

Local Growth Envelopes of Triebel-Lizorkin Spaces of Generalized Smoothness

“…On the other hand, with appropriate assumptions on the functions and N involved-namely, that , N ∈ V, N is strictly increasing and λ 0 N(t) ≤ N(2t), for some λ 0 > 1-the scales of spaces thus defined are the same as the ones defined with the help of sequences, and, as it was shown in [2] in a similar context, one can even choose functions and sequences in such a way that the so-called Boyd indices of both coincide. For this dual way of defining function spaces, we refer also to [1].…”

Real Interpolation of Generalized Besov-Hardy Spaces and Applications

“…Remark 5.4 in [13]). A detailed description how this question can be dealt with in the general case can be found in [2].…”

“…when the parameters p, q are allowed to be less than one) was not investigated in [13] and, to the best of our knowledge, has remained open. Recently, in [3] an approach based on wavelet decompositions obtained in [2] was considered to construct a new retraction with the advantage of working for the full range of the parameters. This method proved to give information about the interpolation spaces for all cases, but, unfortunately, it produced exact interpolation formulas only for power interpolation parameters γ (t) = t θ .…”

Spectral theory for the fractal Laplacian in the context of h-sets

“…This technique was already used by other authors to extend results from classical to generalised smoothness. We refer to [3] and [12]. First we introduce some basic notation related to interpolation.…”