Characterisations of function spaces of generalised smoothness

By Walter Farkas, Hans-Gerd Leopold. 2006

165 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c9f08fbb71cf975bb71b941645b7f64b13868b34

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, methodology): “We refer to [18] and [28] for the treatment of spaces of generalized smoothness.”
On Besov spaces of logarithmic smoothness and Lipschitz spaces (2015, methodology): “See, for example, the papers by DeVore, Riemenschneider and Sharpley [16], Brézis and Wainger [5], Gol’dman [26], Merucci [34], Kalyabin and Lizorkin [32], Cobos and Fernandez [9], Edmunds and Haroske [18], Haroske and Moura [30], Farkas and Leopold [24], Triebel [41, pp. 52–55] and the references g”
Local growth envelopes of spaces of generalized smoothness: the critical case (2004, background): “For a short description of this and some historical remarks, please check [5], where other relevant references can also be found.”
The refined Sobolev scale, interpolation and elliptic problems (2012, unknown): “Leopold [28], P.”
Harmonic analysis of additive Lévy processes (2007, background): “maximal extension S¯ of Ssuch that S¯ : S Ψ(Rd) → S¯(SΨ(Rd)) is a quasi-isometry. The space SΨ(Rd) generalizes further some of the ψ-Bessel potential spaces of Farkas, Jacob, and Schilling (2001) and Farkas and Leopold (2006); see also Jacob and Schilling (2005), Masja and Nagel (1978), and Slobodec”
Besov spaces with variable smoothness and integrability (2010, background): “The paper [17] gives an unified treatment of such spaces following the Fourier analytical approach.”
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 .”