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Greedy bases in variable Lebesgue spaces

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Abstract

We compute the right and left democracy functions of admissible wavelet bases in variable Lebesgue spaces defined on \(\mathbb R^n\). As an application we give Lebesgue type inequalities for these wavelet bases. We also show that our techniques can be easily modified to prove analogous results for weighted variable Lebesgue spaces and variable exponent Triebel–Lizorkin spaces.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama, Tuscaloosa, AL, 35487, USA

    David Cruz-Uribe

  2. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Eugenio Hernández

  3. Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera 13-15, 28049, Madrid, Spain

    José María Martell

Authors
  1. David Cruz-Uribe
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  2. Eugenio Hernández
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  3. José María Martell
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Corresponding author

Correspondence to Eugenio Hernández.

Additional information

Communicated by A. Constantin.

David Cruz-Uribe is supported NSF Grant 1362425. Earlier parts of this project were supported by the Stewart-Dowart fund at Trinity College. Eugenio Hernández and José María Martell are supported in part by MINECO Grant MTM2010-16518 (Spain). Eugenio Hernández has been supported by MINECO Grant 2013-40945-P (Spain). José María Martell has been also supported by ICMAT Severo Ochoa project SEV-2011-0087 (Spain) and he also acknowledges that the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC Agreement No. 615112 HAPDEGMT.

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Cruz-Uribe, D., Hernández, E. & Martell, J.M. Greedy bases in variable Lebesgue spaces. Monatsh Math 179, 355–378 (2016). https://doi.org/10.1007/s00605-015-0862-0

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  • DOI: https://doi.org/10.1007/s00605-015-0862-0

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