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Distance and Measure in Analysis and Partial Differential Equations (Applied and Numerical Harmonic Analysis)

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Publisher Comments:

This comprehensive exploration of a metric approach to some relevant problems and techniques in analysis focuses on examining spaces of homogeneous type. Both the structural and analytical problems under consideration reflect very active areas of current research. The exposition, motivated by examples and details of which many cannot be found elsewhere in book form, unfolds systematically in three parts, starting from such preliminaries as the basic structures of quasi-metric spaces, the homogeneity property and measure theory. More advanced topics are then covered, including Calderón-Zygmund decompositions, L^2 techniques, weighted norm inequalities, BMO, and Hardy spaces. The final aim is to encourage a well-developed way of thinking about some mathematical and even physical problems, i.e. Newtonian and Riesz potentials, fields and their derivatives, mean value and Harnack inequalities related to Hölder regularity, wavelet type analysis on non-euclidian contexts, etc. The book is suitable for self-study or as a classroom resource for graduate students in analysis and PDEs. Real analysis and topology, some basics of Fourier analysis and PDEs are requisite background for the reader.

Product Details

ISBN:
9780817643157
Author:
Aimar, Hugo
Publisher:
Springer
Subject:
Differential Equations
Subject:
Mathematical Analysis
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Measure and Integration
Subject:
abstract harmonic analysis
Subject:
Mathematics-Analysis General
Copyright:
Edition Number:
1
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
March 2007
Binding:
Hardcover
Language:
English
Illustrations:
20 schw.-w. Abb., 20 schw.-w. Zeichn.

Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Functional Analysis

Distance and Measure in Analysis and Partial Differential Equations (Applied and Numerical Harmonic Analysis) New Hardcover
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