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Hardy Spaces on the Euclidean Space

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 057/5 ( reviews)

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Book Synopsis Hardy Spaces on the Euclidean Space by : Akihito Uchiyama

Download or read book Hardy Spaces on the Euclidean Space written by Akihito Uchiyama. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Uchiyama's decomposition of BMO functions is considered the "Mount Everest of Hardy space theory". This book is based on the draft, which the author completed before his sudden death in 1997. Nowadays, his contributions are extremely influential in various fields of analysis, leading to further breakthroughs.

Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces

2015-06-09 Mathematics
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Release : 2015-06-09
Genre : Mathematics
Kind : eBook
Book Rating : 327/5 ( reviews)

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Book Synopsis Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces by : Ryan Alvarado

Download or read book Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces written by Ryan Alvarado. This book was released on 2015-06-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Weighted Hardy Spaces

2014-01-15
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Release : 2014-01-15
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Kind : eBook
Book Rating : 622/5 ( reviews)

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Book Synopsis Weighted Hardy Spaces by : Jan-Olov Stromberg

Download or read book Weighted Hardy Spaces written by Jan-Olov Stromberg. This book was released on 2014-01-15. Available in PDF, EPUB and Kindle. Book excerpt:

Weighted Hardy Spaces

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 074/5 ( reviews)

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Book Synopsis Weighted Hardy Spaces by : Jan-Olov Strömberg

Download or read book Weighted Hardy Spaces written by Jan-Olov Strömberg. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: These notes give the basic ingredients of the theory of weighted Hardy spaces of tempered distribution on Rn and illustrate the techniques used. The authors consider properties of weights in a general setting; they derive mean value inequalities for wavelet transforms and introduce halfspace techniques with, for example, nontangential maximal functions and g-functions. This leads to several equivalent definitions of the weighted Hardy space HPW. Fourier multipliers and singular integral operators are applied to the weighted Hardy spaces and complex interpolation is considered. One tool often used here is the atomic decomposition. The methods developed by the authors using the atomic decomposition in the strictly convex case p>1 are of special interest.

Hardy Spaces on Homogeneous Groups

1982-06-21 Mathematics
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Release : 1982-06-21
Genre : Mathematics
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Book Rating : 10X/5 ( reviews)

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Book Synopsis Hardy Spaces on Homogeneous Groups by : Gerald B. Folland

Download or read book Hardy Spaces on Homogeneous Groups written by Gerald B. Folland. This book was released on 1982-06-21. Available in PDF, EPUB and Kindle. Book excerpt: The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

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