Approximation and entropy numbers in Besov spaces of generalized smoothness

DOI10.1016/j.jat.2007.11.007zbMath1177.47029OpenAlexW2054503189MaRDI QIDQ1041618

Thomas Kühn, Fernando Cobos

Publication date: 3 December 2009

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2007.11.007

zbMATH Keywords

Besov spacescompact embeddingsapproximation numbersentropy numbersgeneralized smoothness

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06)

Related Items (20)

Pointwise characterizations of Besov and Triebel-Lizorkin spaces with generalized smoothness and their applications ⋮ On Besov spaces modelled on Zygmund spaces ⋮ Entropy numbers of functions on \([-1,1\) with Jacobi weights] ⋮ Approximation and entropy numbers of embeddings between approximation spaces ⋮ Schütt's theorem for vector-valued sequence spaces ⋮ Extrapolation estimates for entropy numbers ⋮ On nuclearity of embeddings between Besov spaces ⋮ Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere ⋮ Entropy numbers of embeddings of some 2-microlocal Besov spaces ⋮ Widths of Besov classes of generalized smoothness on the sphere ⋮ Entropy numbers of Besov classes of generalized smoothness on the sphere ⋮ Equivalence of \(K\)- and \(J\)-methods for limiting real interpolation spaces ⋮ Entropy numbers in sequence spaces with an application to weighted function spaces ⋮ On Besov spaces of logarithmic smoothness and Lipschitz spaces ⋮ Entropy numbers of operators acting between vector‐valued sequence spaces ⋮ Some new bounds on the entropy numbers of diagonal operators ⋮ Duality for logarithmic interpolation spaces and applications to Besov spaces ⋮ Gaussian approximation numbers and metric entropy ⋮ Besov spaces with generalized smoothness and summability of multiple Fourier series ⋮ Nikol'skii-type inequalities for entire functions of exponential type in Lorentz-Zygmund spaces

Cites Work

• Entropy numbers of embeddings of weighted Besov spaces
• Entropy numbers in sequence spaces with an application to weighted function spaces
• Inequalities between eigenvalues, entropy numbers, and related quantities of compact operators in Banach spaces
• Entropy numbers, s-numbers, and eigenvalue problems
• Wavelet bases in generalized Besov spaces
• Eigenvalue distribution of compact operators
• Entropy numbers in weighted function spaces. The case of intermediate weights
• Entropy numbers of embeddings of weighted Besov spaces. III: Weights of logarithmic type
• Characterisations of function spaces of generalised smoothness
• Entropy numbers of general diagonal operators
• Entropy Numbers and Approximation Numbers in Function Spacess
• Wavelet bases and entropy numbers in weighted function spaces
• ABSTRACT AND CONCRETE LOGARITHMIC INTERPOLATION SPACES
• !ENTROPY NUMBERS OF EMBEDDINGS OF WEIGHTED BESOV SPACES. II
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