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2023 | Buch

Singular integral operators Kapitel lesen Erstes Kapitel lesen

Analysis in Banach Spaces

Volume III: Harmonic Analysis and Spectral Theory

verfasst von: Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis

Verlag: Springer International Publishing

Buchreihe : Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Inhaltsverzeichnis

Frontmatter
11. Singular integral operators
Abstract
The mapping properties of T will of course heavily depend on the assumptions made on the kernel K that we will discuss in more detail in this chapter.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
12. Dyadic operators and the T (1) theorem
Abstract
Before addressing this question for the Calderón{Zygmund type operators of the kind studied in Chapter 11, we investigate a number of related objects in a simpler dyadic model. Besides serving as an introduction to some of the key techniques, it turns out that these dyadic operators can be, and will be, also used as building blocks of the proper singular integral operators towards the end of the chapter.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
3. The Fourier transform and multipliers
Abstract
In this chapter, we complement the discussion of three major themes of Fourier analysis that we have studied in the previous Volumes.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
4. Function spaces
Abstract
This chapter presents an in-depth study of several classes of vector-valued function spaces defined by smoothness conditions.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
15. Extended calculi and powers of operators
Abstract
In this chapter we address two strongly interwoven topics: How to verify the boundedness of the H∞-calculus of an operator and how to represent and estimate its fractional powers. For concrete operators such as the Laplace operator or elliptic partial differential operators, the fractional domain spaces can often be identifed with certain function spaces considered in Chapter 14 and the imaginary powers of the operator are related to singular integral and pseudo-differential operators treated in Chapters 11 and 13.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
16. Perturbations and sums of operators
Abstract
In this chapter we address a couple of topics in the theory of H∞-calculus centering around the question what can be said about an operator of the form A+B when A and B have certain “good” properties such as being (R-)sectorial or admitting a bounded H∞-calculus.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
17. Maximal regularity
Abstract
The present chapter is one of the central ones of this book project. Maximal regularity provides a link between the general theory of operator-valued singular integrals and the theory of H∞-functional calculus with the regularity theory for evolution equations.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
18. Nonlinear parabolic evolution equations in critical spaces
Abstract
As we have seen in the preceding sections, in the context of inhomogeneous linear evolution equations, maximal regularity enables one to set up an isomorphism between the space of data (initial value and inhomogeneity) and the solution space.
Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis
Backmatter
Metadaten
Titel
Analysis in Banach Spaces
verfasst von
Tuomas Hytönen
Jan van Neerven
Mark Veraar
Lutz Weis
Copyright-Jahr
2023
Electronic ISBN
978-3-031-46598-7
Print ISBN
978-3-031-46597-0
DOI
https://doi.org/10.1007/978-3-031-46598-7