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Reports necessary conditions for solvability in weighted Lp spaces, suggesting new insights into infinite zeros in weights.
We study a Riemann–Hilbert boundary value problem in the upper half-plane within the weighted space Lᵖ(ρ) , where 1<p<∞ and the weight ρ admits infinitely many zeros. Necessary and sufficient conditions are obtained for normal solvability and for the associated operator to be Noetherian, extending the classical finite-index theory to weights with infinitely many zeros. Explicit solution formulas are derived for both homogeneous and inhomogeneous problems, with special attention to the case of negative index.
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S. Aghekyan (2026) studied this question.
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