Pavlovic / Pavlovic Function Classes on the Unit Disc

An Introduction
1. Auflage 2013
ISBN: 978-3-11-028190-3
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 52, 462 Seiten

Reihe: De Gruyter Studies in Mathematics

Autoren/Hrsg.

Pavlovic, Miroslav

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Preface 1 Quasi-Banach spaces 1.1 Quasinorm and p-norm 1.2 Linear operators 1.3 The closed graph theorem The open mapping theorem The uniform boundedness principle The closed graph theorem 1.4 F-spaces 1.5 The spaces lp 1.6 Spaces of analytic functions 1.7 The Abel dual of a space of analytic functions 1.7a Homogeneous spaces 2 Interpolation and maximal functions 2.1 The Riesz/Thorin theorem 2.2 Weak Lp-spaces and Marcinkiewicz’s theorem 2.3 The maximal function and Lebesgue points 2.4 The Rademacher functions and Khintchine’s inequality 2.5 Nikishin’s theorem 2.6 Nikishin and Stein’s theorem 2.7 Banach’s principle, the theorem on a.e. convergence, and Sawier’s theorems 2.8 Addendum: Vector-valued maximal theorem 3 Poisson integral 3.1 Harmonic functions 3.1a Green’s formulas 3.1b The Poisson integral 3.2 Borel measures and the space h1 3.3 Positive harmonic functions 3.4 Radial and non-tangential limits of the Poisson integral 3.4a Convolution of harmonic functions 3.5 The spaces hp and Lp(T) 3.6 A theorem of Littlewood and Paley 3.7 Harmonic Schwarz lemma 4 Subharmonic functions 4.1 Basic properties 4.1a The maximum principle 4

Über Autor(innen)

Miroslav Pavlovic, University of Belgrade, Serbia.