Titlebook: New Trends in Applied Harmonic Analysis, Volume 2; Harmonic Analysis, G Akram Aldroubi,Carlos Cabrelli,Ursula Molter Book 2019 Springer Nat

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https://doi.org/10.1007/978-3-030-32353-0Harmonic Analysis math; Harmonic Analysis book; Harmonic Analysis trends; Applied harmonic analysis; Geo

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Hardy Spaces with Variable Exponents,In this paper, we make a survey on some recent developments of the theory of Hardy spaces with variable exponents in different settings.

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Gabor Frames: Characterizations and Coarse Structure,This chapter offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice.

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,Sharp Quantitative Weighted , Estimates and a New Proof of the Harboure–Macías–Segovia’s ExtrapolatIn this paper, we are concerned with quantitative weighted .-type estimates. We provide a new quantitative proof for a result due to Harboure, Macías and Segovia (Amer J Math 110 (1988), 383–397, [.]) that also allows to slightly weaken the hypothesis. We also obtain some sharp weighted .-type estimates for Calderón–Zygmund operators.

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Regularity of Maximal Operators: Recent Progress and Some Open Problems, the current open problems in the topic. Overall, a list of fifteen research problems is presented. It summarizes the contents of a talk delivered by the author in the CIMPA 2017 Research School—Harmonic Analysis, Geometric Measure Theory, and Applications, in Buenos Aires, Argentina.

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On the Approximate Unit Distance Problem,stance is . for any .. The best known bound is .. We show that if the set under consideration is homogeneous, or, more generally, .-adaptable in the sense of [.], and the fixed distance is much smaller than the diameter of the set, then the exponent . is significantly improved, even if we consider a

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Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets,mphasis on estimates of the Hausdorff dimension of exceptional sets and on restricted projection families. We shall also discuss relations between projections and Hausdorff dimension of Besicovitch sets.