| 书目名称 | Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces | | 副标题 | A Sharp Theory | | 编辑 | Ryan Alvarado,Marius Mitrea | | 视频video | | | 概述 | Problems of the sort considered in the present monograph profoundly affect the nature of the results in many other adjacent areas of mathematics..Includes supplementary material: | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | .Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces. The text is divided into two main parts, with the first part providing atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-cont | | 出版日期 | Book 2015 | | 关键词 | 43A17,43A85,54E35,54E50,46A16,46F05; Atoms; Grand maximal function; Hardy space; Quasi-metric space; Spac | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-18132-5 | | isbn_softcover | 978-3-319-18131-8 | | isbn_ebook | 978-3-319-18132-5Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer International Publishing Switzerland 2015 |
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发表于 2025-3-21 16:20:50
