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Báo cáo hóa học: "BOUNDARY BEHAVIOUR OF ANALYTIC FUNCTIONS IN SPACES OF DIRICHLET TYPE"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: BOUNDARY BEHAVIOUR OF ANALYTIC FUNCTIONS IN SPACES OF DIRICHLET TYPE | BOUNDARY BEHAVIOUR OF ANALYTIC FUNCTIONS IN SPACES OF DIRICHLET TYPE DANIEL GIRELA AND JOSE ANGEL PELAEZ Received 24 June 2005 Revised 11 October 2005 Accepted 8 November 2005 For 0 p 00 and a -1 we let Ví be the space of all analytic functions f in D z e C z 1 such that f belongs to the weighted Bergman space A . We obtain a number of sharp results concerning the existence of tangential limits for functions in the spaces G a. We also study the size of the exceptional set E f ei0 e dD V f 0 ooi where V f 0 denotes the radial variation of f along the radius 0 ei0 for functions f e a. Copyright 2006 D. Girela and J. A. Pelaez. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and main results Let D denote the open unit disk of the complex plane C. If 0 r 1 and f is an analytic function in D abbreviated f e Xol D we set 1 j-2n 1 p Mp r f 21 f rẽ pdt Ip r f Mp r f 0 p o 2n 0 Mo r f sup f re 5 . 0 t 2n 1.1 For 0 p o the Hardy space Hp consists of those functions f e GXol D for which II f IIhp f sup0 r 1 Mp r f o. We refer to 10 for the theory of Hardy spaces. The weighted Bergman space Ap 0 p o a -1 is the space of all functions f e ol D such that 1 p IIf u f JD 1 - z a f z pdA z j o 1.2 where dA z 1 n dxdy denotes the normalized Lebesgue area measure in D. We mention 11 16 as general references for the theory of Bergman spaces. Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 92795 Pages 1-12 DOI 10.1155 JIA 2006 92795 2 Boundary behaviour We will write a 0 p 00 a -1 for the space of all functions f G Xol D such that JD 1 - z a f z p dA z 00. In other words f G a f G Ap. 1.3 If p a 1 it is well known that a Ap-p with equivalence of norms see 12 Theorem 6 . If p 1 and a p - 2 we are considering the Besov spaces p which have been extensively studied in