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Hardy spaces and integral formulas for đâ±đ©âdomains with arbitrary boundary
Author(s) -
Bauer Wolfram
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610631
Subject(s) - mathematics , holomorphic function , boundary (topology) , bergman space , hardy space , bounded function , pure mathematics , banach space , space (punctuation) , mathematical analysis , linguistics , philosophy
Let E be the dual of a FrĂ©chet nuclear space, then it is wellâknown that for each open set U in E the space â( U ) of all holomorphic functions on U is a nuclear FrĂ©chet space. Let be a commutative unital Banach subâalgebra of all bounded holomorphic functions on U which separates points. Applying the nuclearity of â( U ) we show that the evaluation on U is given by an integral formula over the Shilov boundary of . We obtain Szegöâ and Bergman kernels together with some boundary estimates. Moreover, we show that there is a notion of Hardy and Bergman space for â±âdomains with arbitrary boundary. (© 2008 WILEYâVCH Verlag GmbH & Co. KGaA, Weinheim)