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Explicit Riemann‐Hilbert problems in Hardy spaces
Author(s) -
Semmler Gunter
Publication year - 2011
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.200710135
Subject(s) - mathematics , hardy space , holomorphic function , smoothness , class (philosophy) , pure mathematics , mathematical analysis , boundary (topology) , unit circle , unit (ring theory) , mathematics education , artificial intelligence , computer science
This paper is concerned with boundary value problems for holomorphic functions in the unit disc, where the boundary condition is given by an explicit equation for the real and imaginary part of the solution on the unit circle. Relaxing the smoothness assumptions in well‐known results for problems of this type we can still prove the solvability in Hardy spaces H p for continuous right‐hand sides where p depends on the at most linear growth of the restriction curves. We introduce the notion wrapping solution for a class of functions that has no counterpart in the theory where the solvability is considered only in the class of functions extending continuously onto the closed unit disc. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim