Yang / Hu The Hardy Space H1 with Non-doubling Measures and Their Applications

Erscheinungsjahr 2014
ISBN: 978-3-319-00825-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2084, 653 Seiten, eBook

Reihe: Lecture Notes in Mathematics

The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems. The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.

Zielgruppe

Research

Autoren/Hrsg.

Yang, Dachun

Yang, Dongyong

Hu, Guoen

Inhaltsverzeichnis

Preliminaries.- Approximations of the Identity.- The Hardy Space H1 ( µ ).- The Local Atomic Hardy Space h1 ( µ ).- Boundedness of Operators over (R D , µ ).- Littlewood-Paley Operators and Maximal Operators Related to Approximations of the Identity.- The Hardy Space H 1 (?, ?)and Its Dual Space RBMO (?, ?).- Boundedness of Operators over((?, ?).- Bibliography.- Index.- Abstract.