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<p>We prove both necessary and sufficient conditions for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-boundedness of certain multilinear generalized Radon transforms that arise as Heisenberg group analogues of the Brascamp–Lieb inequalities on Euclidean space. The necessary and sufficient conditions coincide in some important special cases, but differ in others.</p>

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Inequalities of Brascamp–Lieb type on the Heisenberg group

  • 期刊论文

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  • 发表日期：

    2025年10月27日

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  • Kaiyi Huang,
  • Betsy Stovall

摘要

We prove both necessary and sufficient conditions for \(L^p\) L p -boundedness of certain multilinear generalized Radon transforms that arise as Heisenberg group analogues of the Brascamp–Lieb inequalities on Euclidean space. The necessary and sufficient conditions coincide in some important special cases, but differ in others.