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<p>In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(z^k\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>z</mi> <mi>k</mi> </msup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k \in \mathbb {N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math></EquationSource> </InlineEquation>. Applications to sharp higher order Poincaré inequalities and other related extremal problems are discussed.</p>

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Sharp Embeddings Between Weighted Paley-Wiener Spaces

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Emanuel Carneiro,
  • Cristian González-Riquelme,
  • Lucas Oliveira,
  • Andrea Olivo,
  • Sheldy Ombrosi,
  • Antonio Pedro Ramos,
  • Mateus Sousa

摘要

In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by \(z^k\) z k , \(k \in \mathbb {N}\) k ∈ N . Applications to sharp higher order Poincaré inequalities and other related extremal problems are discussed.