Geometric Harmonic Analysis II: Function Spaces Measuring Size and Smoothness on Rough Sets

This monograph is part of a larger program to develop tools in Real and Harmonic Analysis for geometric measure theoretic flavor, treating boundary value problems in general geometric and analytic settings. Volume II focuses on function spaces measuring size and smoothness, highlighting the interplay between differentiability properties and singular integral operators. It is intended for researchers, graduate students, and industry professionals.

Format: Hardback
Length: 930 pages
Publication date: 04 March 2023
Publisher: Springer International Publishing AG

This comprehensive monograph forms a vital component of a larger program, envisioned in five volumes, with the primary objective of developing robust tools in Real and Harmonic Analysis, possessing a geometric measure theoretic flavor. These tools will be capable of addressing a wide range of boundary value problems formulated in diverse geometric and analytic contexts.

Volume II specifically focuses on function spaces that measure size and/or smoothness, including notable examples such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, and more. Within this volume, significant attention is given to the intricate interplay between differentiability properties of functions and singular integral operators.

The text is meticulously crafted to cater to the needs of researchers, graduate students, and industry professionals who have a deep interest in harmonic analysis, functional analysis, geometric measure theory, and function space theory. It provides a comprehensive and authoritative exploration of the latest developments and applications in these fields, making it an invaluable resource for scholars and practitioners alike.

Weight: 1586g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031137174
Edition number: 1st ed. 2022