Function spaces of generalised smoothness

By S. D. Moura. 2001

95 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8d6a24e18bccec1500e782dc41bf0cf4b061fa37

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Characterisations of function spaces of generalised smoothness (2006, background): “F (s,Ψ) p,q considered in [Mo99] and [ Mo01 ].”
A note on wavelet bases in function spaces (2004, background): “A detailed account of these spaces has been given in [20], including atoms and local means.”
Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, background): “Later on, spaces of generalized smoothness appeared in interpolation theory and have been investigated in [10, 36] and [39].”
2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability (2009, background): “Moreover, also the spaces of generalized smoothness are contained in this approach ([11], [23]) by taking wj(x) = 2 jsΨ(2−j) , or more general wj(x) = σj .”
Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis (2008, background): “Furthermore, this concept was extended and generalised to (d, Ψ)-sets in [9], [10], [30], h-sets in [4], anisotropic d-sets in [13], [48], but this is out of the scope of the present paper.”
Local growth envelopes of spaces of generalized smoothness: the critical case (2004, background): “2 The above spaces, quasi-normed by (11) and (12), were introduced by Edmunds and Triebel in [3, 4] and also considered by Moura in [10, 11], where they have remarked that such spaces are independent of the resolution of unity taken, in the sense of equivalent quasi-norms.”
The refined Sobolev scale, interpolation and elliptic problems (2012, unknown): “Moura [91], B.”
Wavelet bases in generalized Besov spaces (2005, background): “We refer to [15] for a systematic study on spaces B ) pq .”