书目名称 | Suprematism in Harmonic Analysis | 编辑 | Antonio Córdoba | 视频video | http://file.papertrans.cn/886/885293/885293.mp4 | 概述 | Winner of the Ferran Sunyer i Balaguer Prize for the best monograph 2024.Proves the Kakeya maximal function theorem.Offers an in-depth exploration of crucial topics in harmonic analysis | 丛书名称 | Progress in Mathematics | 图书封面 |  | 描述 | .This award-winning monograph explores advanced topics in harmonic analysis, addressing both classical and contemporary problems. Several connections to number theory, crystallography or atomic theory are also surveyed. The term “suprematism” refers to a certain geometric point of view underlying proofs and arguments...The opening of the book is dedicated to a few results, with short statements and proofs, that could be called “mathematical haikus”. Then, in the first part of the book, singular integrals beyond the classical Calderón-Zygmund theory, such as Vitali-type covering lemmas and estimates for the corresponding maximal operators, are explored. The exponential overlapping of parallelepipeds, the strong maximal function, and Zygmund‘s conjecture about monotonic bases are also covered. The core of this part is devoted to the Kakeya maximal function and its relation to the spherical summation of Fourier series and integrals. The two-dimensional case is well understood, but the case of higher dimensions still presents many open problems and conjectures. The chapters in the second part of the book treat questions at the interface of harmonic analysis and number theory, including | 出版日期 | Book 2024 | 关键词 | Harmonic analysis; Hilbert transforms; Euclidean space; Basicovitch sets; Kakeya maximal function theore | 版次 | 1 | doi | https://doi.org/10.1007/978-3-031-73737-4 | isbn_softcover | 978-3-031-73739-8 | isbn_ebook | 978-3-031-73737-4Series ISSN 0743-1643 Series E-ISSN 2296-505X | issn_series | 0743-1643 | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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