Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
THE DIRICHLET SPACE: A SURVEY NICOLA ARCOZZI, RICHARD ROCHBERG, ERIC T. SAWYER, AND BRETT D. WICK
 

Summary: THE DIRICHLET SPACE: A SURVEY
NICOLA ARCOZZI, RICHARD ROCHBERG, ERIC T. SAWYER, AND BRETT D. WICK
Abstract. In this paper we survey many results on the Dirichlet space of
analytic functions. Our focus is more on the classical Dirichlet space on the
disc and not the potential generalizations to other domains or several variables.
Additionally, we focus mainly on certain function theoretic properties of the
Dirichlet space and omit covering the interesting connections between this
space and operator theory. The results discussed in this survey show what is
known about the Dirichlet space and compares it with the related results for
the Hardy space.
Contents
1. Introduction 2
2. The Dirichlet Space 2
2.1. The Definition 2
2.2. The Definition in terms of Boundary Values and other Characterizations
of the Dirichlet Norm 5
2.3. The Reproducing Kernel 6
3. Carleson measures 6
3.1. Definition and the Capacitary Characterization 6
3.2. Characterizations by Testing Conditions 9

  

Source: Arcozzi, Nicola - Dipartimento di Matematica, UniversitÓ di Bologna

 

Collections: Mathematics