Overview

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.

Full Product Details

Author:   Dorina Mitrea ,  Irina Mitrea ,  Marius Mitrea
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2022
Volume:   73
Weight:   1.586kg
ISBN:  

9783031137174

ISBN 10:   3031137175
Pages:   930
Publication Date:   04 March 2023
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

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.-  A. Terms and Notation Used in Volume II. References.- Index.

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