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Abstract <p> New weighted spaces of the Hardy–Littlewood type of continuous functions defined indomains with piecewise smooth boundaries are introduced, and their structural properties aredescribed. It is established that these spaces contain functions representable by generalizedintegrals of the Cauchy type with homogeneous kernels of degree <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-1\)</EquationSource> </InlineEquation>. The latter circumstance opens up the possibilityof using these spaces for solving elliptic systems of the first and second order with continuouscoefficients.</p>

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Weighted Hardy–Littlewood Spaces in Piecewise Smooth Domains

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. P. Soldatov

摘要

Abstract

New weighted spaces of the Hardy–Littlewood type of continuous functions defined indomains with piecewise smooth boundaries are introduced, and their structural properties aredescribed. It is established that these spaces contain functions representable by generalizedintegrals of the Cauchy type with homogeneous kernels of degree \(-1\) . The latter circumstance opens up the possibilityof using these spaces for solving elliptic systems of the first and second order with continuouscoefficients.