Titlebook: Recent Advances in Harmonic Analysis and Applications; In Honor of Konstant Dmitriy Bilyk,Laura De Carli,Brett D. Wick Conference proceedin

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A Survey of Multidimensional Generalizations of Cantor’s Uniqueness Theorem for Trigonometric Seriesmension ., .≥2, we begin by assuming that for each . in [0,2π)., ∑....=0 where . and .. It is quite natural to group together all terms whose indices differ only by signs. But here there are still several different natural interpretations of the infinite multiple sum, and, correspondingly, several d

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Multiparameter Projection Theorems with Applications to Sums-Products and Finite Point Configuration, where . is a subset of the real line of a given Hausdorff dimension, . and . ⋅.={ . ⋅. :.,.∈.}. We also use projection results and inductive arguments to show that if a Hausdorff dimension of a subset of .. is sufficiently large, then the .-dimensional Lebesgue measure of the set of .-simplexes de

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Riesz Potentials, Bessel Potentials, and Fractional Derivatives on Besov-Lipschitz Spaces for the Gan detail in Gatto and Urbina (On Gaussian Lipschitz Spaces and the Boundedness of Fractional Integrals and Fractional Derivatives on them, 2009. Preprint. arXiv:0911.3962v2). In this chapter we will study the boundedness of those operators on Gaussian Besov-Lipschitz spaces ...(γ.). Also, these resu

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Maximal Operators Associated to Sets of Directions of Hausdorff and Minkowski Dimension Zerois given by . In this chapter we show that if .. is bounded on ..(ℝ.) for 1<.≤., then . must be countable and of Hausdorff and Minkowski dimension zero. We shall see that the converse does not hold, however, by exhibiting an example of a countable set . of Hausdorff and Minkowski dimension zero for

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On Fubini Type Property in Lorentz Spaces coordinate axes belong to ., and their one-dimensional ..-norms belong to . We show that for . ≠ . it does not imply that . (this complements one result by Cwikel). Conversely, we assume that ., and we show that then for . < . almost all linear sections of . belong to ., but for . < . all linear se

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ary and style issues to writing research papers and for acad.This book is for university students, with at least a mid-intermediate level of English...It is designed both for self-study and also as a support for a course on academic communication. It can thus be used alongside the companion volumes: