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Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces: A Sharp Theory (Lecture Notes in Mathematics, nr. 2142)

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en Limba Engleză Paperback – 25 Jun 2015
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.
 
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Specificații

ISBN-13: 9783319181318
ISBN-10: 3319181319
Pagini: 450
Ilustrații: 5 schwarz-weiße und 12 farbige Abbildungen, Bibliographie
Dimensiuni: 155 x 235 x 30 mm
Greutate: 0.74 kg
Ediția: 2015
Editura: Springer
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării: Cham, Switzerland

Public țintă

Research

Cuprins

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.

Textul de pe ultima copertă

Systematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives 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 an audience of mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.

Caracteristici

Problems of the sort considered in the present monograph profoundly affect the nature of the results in many other adjacent areas of mathematics.