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Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces - A Sharp Theory (Paperback, 2015 ed.)
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Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces - A Sharp Theory (Paperback, 2015 ed.)
Series: Lecture Notes in Mathematics, 2142
Expected to ship within 10 - 15 working days
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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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