DIRICHLET BOUNDARY VALUE PROBLEMIN THE WEIGHTED SPACESL1(ρ)

Author(s)

DIRICHLET BOUNDARY VALUE PROBLEMIN THE WEIGHTED SPACESL1(ρ) Vahee Petrosian

The Dirichlet boundary value problem in the weighted spacesL1(ρ)on theunit circleT={z:|z|=1}is investigated, whereρ(t) =|t−tk|αk,k=1,...,m,tk∈Tandαkare arbitrary real numbers. The problem is to determine a functionΦ(z)analytic in unit disc such that: limr→1−0‖ReΦ(rt)−f(t)‖L1(ρr)=0,wheref∈L1(ρ). In the paper necessary and sufficient conditions for solvability ofthe problem are given and the general solution is written in the explicit form.

DOI: 10.46991/PYSU:A/2017.51.3.250 Physical and Mathematical Sciences, 51(3 (244) 250-254

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Keywords

Dirichlet problem, weighted spaces, Cauchy type integral.

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