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Approximation and Entropy Numbers of Embeddings Between Approximation Spaces

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Abstract

We consider general linear approximation spaces \(X^b_q\) based on a quasi-Banach space X, and we analyze the degree of compactness of the embedding \(X^b_q \hookrightarrow X\). Applications are given to periodic Besov spaces on the d-torus, including spaces of generalized and logarithmic smoothness. In particular, we obtain the exact asymptotic behavior of approximation and entropy numbers of embeddings of such Besov spaces in Lebesgue spaces and in Besov spaces of logarithmic smoothness.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040, Madrid, Spain

    Fernando Cobos

  2. Department of Mathematics, Center for Mathematics of the University of Coimbra (CMUC), 3001-454, Coimbra, Portugal

    Óscar Domínguez

  3. Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109, Leipzig, Germany

    Thomas Kühn

Authors
  1. Fernando Cobos
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  2. Óscar Domínguez
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  3. Thomas Kühn
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Corresponding author

Correspondence to Fernando Cobos.

Additional information

Communicated by Pencho Petrushev.

The authors have been supported in part by the Spanish Ministerio de Economía y Competitividad (MTM2013-42220-P). O. Domínguez has also been supported by the FPU Grant AP2012-0779 of the Ministerio de Economía y Competitividad.

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Cobos, F., Domínguez, Ó. & Kühn, T. Approximation and Entropy Numbers of Embeddings Between Approximation Spaces. Constr Approx 47, 453–486 (2018). https://doi.org/10.1007/s00365-017-9383-5

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  • DOI: https://doi.org/10.1007/s00365-017-9383-5

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