Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces : A Sharp Theory / by Ryan Alvarado, Marius Mitrea.

Format:

Book

Author/Creator:

Alvarado, Ryan, author.

Mitrea, Marius, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2142.

Lecture Notes in Mathematics, 0075-8434 ; 2142

Language:

English

Subjects (All):

Fourier analysis.

Mathematics.

Functional analysis.

Differential equations, Partial.

Fourier Analysis.

Real Functions.

Functional Analysis.

Measure and Integration.

Partial Differential Equations.

Local Subjects:

Fourier Analysis.

Real Functions.

Functional Analysis.

Measure and Integration.

Partial Differential Equations.

Physical Description:

1 online resource (VIII, 486 pages 17 illustrations, 12 illustrations in color).

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783319181325

Access Restriction:

Restricted for use by site license.