Besov spaces with positive smoothness on Rn, embeddings and growth envelopes

Authors:
Dorothee D. Haroske;Cornelia Schneider
Affiliations:
Mathematical Institute, Friedrich-Schiller-University Jena, D-07737 Jena, Germany;University Leipzig, PF 100920, D-04009 Leipzig, Germany
Venue:
Journal of Approximation Theory
Year:
2009

Citing 2
Cited 2

Spectral theory and differential operators

Spectral theory and differential operators
Interpolation of operators

Interpolation of operators

Full length article: Approximation schemes satisfying Shapiro's Theorem

Journal of Approximation Theory
Full length article: Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We characterise Besov spaces with positive smoothness on R^n, obtained by different approaches. First we present two settings B"p","q^s(R^n), B"p","q^s(R^n) associated to definitions by differences and Fourier-analytical methods and give an equivalent characterisation in terms of subatomic decompositions for the spaces B"p","q^s. We study their connections and diversity, as well as embeddings between Besov spaces and into Lorentz spaces. Secondly, we determine their growth envelopes E"G(B"p","q^s(R^n)) for 00, and finally discuss some applications.