A Nonlinear Functional on the Dirichlet Space

A Nonlinear Functional on the Dirichlet Space

The nonlinear functional Λ1(f) = (1/2π) ∫2π0e|f(eiθ|2dθ was shown by Chang and Marshall to be bounded on the unit ball B of the space D of analytic functions in the unit disk with finite Dirichlet integral. We show that Λ1 is weakly continuous on B except at zero and that Λ1 attains its maximum over...

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Veröffentlicht in:Journal of mathematical analysis and applications 1995-04, Vol.191 (2), p.380-401
Hauptverfasser: Cima, J., Matheson, A.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Functions of a complex variable
Mathematical analysis
Mathematics
Potential theory
Sciences and techniques of general use
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Zusammenfassung:The nonlinear functional Λ1(f) = (1/2π) ∫2π0e|f(eiθ|2dθ was shown by Chang and Marshall to be bounded on the unit ball B of the space D of analytic functions in the unit disk with finite Dirichlet integral. We show that Λ1 is weakly continuous on B except at zero and that Λ1 attains its maximum over a subset of B determined by kernel functions.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1995.1136