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- Title
INVERSE IMAGES OF SECTORS BY FUNCTIONS IN WEIGHTED BERGMAN--ORLICZ SPACES.
- Authors
Pérez-González, Fernando; Fernández, Julio C. Ramos
- Abstract
For ϵ > 0, let Σϵ = {z ϵ ℂ : ∣arg z∣ < ϵ}. It has been proved (D. E. Marshall and W. Smith, Rev. Mat. Iberoamericana 15 (1999), 93-116) that ∫f-1(Σϵ) ∣ƒ (z)∣ dA (z)≃ ∫D ∣ƒ(z)∣ dA (z) for every ϵ > 0, uniformly for every univalent function f in the classical Bergman space A1 that fixes the origin. In this paper, we extend this result to those conformal maps on D belonging to weighted Bergman-Orlicz classes such that ƒ (0) = ∣ ƒ'(0)∣ - 1 = 0.
- Subjects
ORLICZ spaces; BERGMAN spaces; FUNCTION spaces; FUNCTIONAL analysis; FUNCTIONAL equations; INTEGRAL equations; CALCULUS of variations; FUNCTIONS of several complex variables; MATHEMATICAL analysis; NUMERICAL analysis
- Publication
Journal of the Australian Mathematical Society, 2009, Vol 86, Issue 2, p233
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788708000517