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<p>We prove sharp <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> </InlineEquation>-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^q\)</EquationSource> </InlineEquation>-estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. We apply this to the Limiting Absorption Principle for elliptic (pseudo-)differential operators with constant coefficients. In this way we obtain a richer existence theory for Helmholtz-type problems on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> </InlineEquation> with block-radial right hand sides.</p>

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The restriction-extension operator on Lebesgue spaces with symmetries and applications to the limiting absorption principle

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  • 发表日期：

    2026年8月3日

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  • Rainer Mandel

摘要

We prove sharp \(L^p\) - \(L^q\) -estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. We apply this to the Limiting Absorption Principle for elliptic (pseudo-)differential operators with constant coefficients. In this way we obtain a richer existence theory for Helmholtz-type problems on \(\mathbb {R}^d\) with block-radial right hand sides.