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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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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