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Efendiyev, M.A. ; Russ, E.*

Hardy spaces for the conjugated Beltrami equation in a doubly connected domain.

J. Math. Anal. Appl. 383, 439-450 (2011)
Postprint DOI
Open Access Green
We consider Hardy spaces associated to the conjugated Beltrami equation on doubly connected planar domains. There are two main differences with previous studies (Baratchart et al.. 2010 [2]). First, while the simple connectivity plays an important role in Baratchart et al. (2010) [2], the multiple connectivity of the domain leads to unexpected difficulties. In particular, we make strong use of a suitable parametrization of an analytic function in a ring by its real part on one part of the boundary and by its imaginary part on the other. Then, we allow the coefficient in the conjugated Beltrami equation to belong to W(1,q) for some q is an element of (2, +infinity right perpendicular, while it was supposed to be Lipschitz in Baratchart et al. (2010) [2]. We define Hardy spaces associated with the conjugated Beltrami equation and solve the corresponding Dirichlet problem. The same problems for generalized analytic function are also solved.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Hardy spaces; Doubly connected domain; Dirichlet problem; Analytic projection
ISSN (print) / ISBN 0022-247X
e-ISSN 1096-0813
Zeitschrift Journal of Mathematical Analysis and Applications
Quellenangaben Band: 383, Heft: 2, Seiten: 439-450 Artikelnummer: , Supplement: ,
Verlag Elsevier
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biomathematics and Biometry (IBB)