Riemann problem in the weighted spaces L1(ρ)
- Authors: Hayrapetyan H.M.1, Petrosyan V.G.1
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Affiliations:
- Yerevan State University
- Issue: Vol 51, No 5 (2016)
- Pages: 249-261
- Section: Real and Complex Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/227963
- DOI: https://doi.org/10.3103/S106836231605006X
- ID: 227963
Cite item
Abstract
In the unit disc bounded by the circle T = {z, |z| = 1} we consider the Riemann boundary value problem in the weighted space L1(ρ), where
\(\rho \left( t \right) = {\prod\nolimits_{k = 1}^m {\left| {t - {t_k}} \right|} ^{{\alpha _k}}}\)
, tk ∈ T, k = 1, 2,..., m, and αk, k = 1, 2,..., m are real numbers. The question of interest is to determine an analytic outside the circle T function ϕ(z), ϕ(∞) = 0 to satisfy \({\lim _{r \to 1 - 0}}||{\Phi ^ + }\left( {rt} \right) - a\left( t \right){\Phi ^ - }\left( {{r^{ - 1}}t} \right) - f\left( t \right)|{|_{{L^1}\left( {{\rho _r}} \right)}} = 0\)
, where f ∈ L1(ρ), a(t) ∈ Cδ(T), δ>0, and ρr are some continuations of function ρ inside the circle. The normal solvability of this problem is established.About the authors
H. M. Hayrapetyan
Yerevan State University
Author for correspondence.
Email: hhayrapet@gmail.com
Armenia, Yerevan
V. G. Petrosyan
Yerevan State University
Email: hhayrapet@gmail.com
Armenia, Yerevan