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Abstract <p>We study a Riemann–Hilbert boundary value problem in the upper half-plane within the weighted space <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^{p}(\rho)\)</EquationSource> <!--ContMath2560111Aghekyan-m3--> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(1&lt;p&lt;\infty\)</EquationSource> <!--ContMath2560111Aghekyan-m4--> </InlineEquation> and the weight <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\rho\)</EquationSource> <!--ContMath2560111Aghekyan-m5--> </InlineEquation> 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.</p>

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On a Riemann–Hilbert Boundary Value Problem in Weighted \(\boldsymbol{L^{p}}\) Spaces

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  • 发表日期：

    2026年4月18日

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  • S. Aghekyan

摘要

Abstract

We study a Riemann–Hilbert boundary value problem in the upper half-plane within the weighted space \(L^{p}(\rho)\) , where \(1<p<\infty\) and the weight \(\rho\) 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.