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Modulation Spaces pp 107–117Cite as

Birkhäuser

Weighted Modulation Spaces

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The concept of weight function appears ubiquitously in harmonic analysis. A weight is a nonnegative measurable function that, depending on the context, quantifies more precisely growth, decay, or smoothness. A classic example in the linear and multilinear Calderón-Zygmund theory is played by the nowadays well-understood A p classes of weights of Muckenhoupt-Wheeden which give natural weighted norm inequalities on Lebesgue spaces for the maximal operator, singular integrals, and much more. The A p-weights are intrinsically connected to reverse Hölder inequalities and they were from their inception important in the theory of conformal mappings and boundary-value problems for the Laplace equation on a bounded domain with Lipschitz boundary; see García-Cuerva and Rubio de Francia (Weighted Norm Inequalities and Related Topics. Elsevier, North-Holland, 1985) for more details about these topics. The special interest in the A 2-class and the subsequent settling of the so-called A 2-conjecture by Hytönen (Ann Math 175(3):1473–1506, 2012) came amid a flurry of works that introduced new ideas and techniques to this area of research.

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Authors and Affiliations

  1. Department of Mathematics, Western Washington University, Bellingham, WA, USA

    Árpád Bényi

  2. Department of Mathematics, University of Maryland, College Park, MD, USA

    Kasso A. Okoudjou

Authors
  1. Árpád Bényi
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  2. Kasso A. Okoudjou
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Bényi, Á., Okoudjou, K.A. (2020). Weighted Modulation Spaces. In: Modulation Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-0716-0332-1_5

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