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Autor: Ryan Alvarado
ISBN-13: 9783319181318
Einband: Taschenbuch
Seiten: 486
Gewicht: 1012 g
Format: 236x155x27 mm
Sprache: Englisch

Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces

.2142, Lecture Notes in Mathematics
A Sharp Theory
Introduction. - Geometry of Quasi-Metric Spaces.- Analysis on Spaces of Homogeneous Type.- Maximal Theory of Hardy Spaces.- Atomic Theory of Hardy Spaces.- Molecular and Ionic Theory of Hardy Spaces.- Further Results.- Boundedness of Linear Operators Defined on Hp(X).- Besov and Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces.
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-contained and is intended for mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.
Autor: Ryan Alvarado
ISBN-13:: 9783319181318
ISBN: 3319181319
Verlag: Springer, Berlin, Springer International Publishing, Springer
Gewicht: 1012g
Seiten: 486
Sprache: Englisch
Auflage 2015
Sonstiges: Taschenbuch, 236x155x27 mm, 5 SW-Abb., 12 Farbabb.