Geometric Harmonic Analysis II Function Spaces Measuring Size and Smoothness on Rough Sets 1st Edition by Dorina Mitrea, Irina Mitrea, Marius Mitrea 3031137181 9783031137181

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Product details:

ISBN 10: 3031137181 

ISBN 13: 9783031137181

Author:  Dorina Mitrea, Irina Mitrea, Marius Mitrea 

This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.

Geometric Harmonic Analysis II Function Spaces Measuring Size and Smoothness on Rough Sets 1st Table of contents:

1. Preliminary Functional Analytic Matters
2. Abstract Fredholm Theory
3. Functions of Vanishing Mean Oscillations and Vanishing Hölder Moduli
4. Hardy Spaces on Ahlfors Regular Sets
5. Banach Function Spaces, Extrapolation, and Orlicz Spaces
6. Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets
7. Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets
8. Boundary Traces from Weighted Sobolev Spaces into Besov Spaces
9. Besov and Triebel-Lizorkin Spaces in Open Sets
10. Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morrey Spaces
11. Sobolev Spaces on the Geometric Measure Theoretic Boundary of Sets of Locally Finite Perimeter

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Tags: Geometric Harmonic, Function Spaces, Measuring Size, Smoothness, Dorina Mitrea, Irina Mitrea, Marius Mitrea