We investigate so-called Laplace–Carleson embeddings for large exponents. In particular, we extend some results by Jacob, Partington, and Pott. We also discuss some related results for Sobolev– and Besov spaces, and mapping properties of the Fourier transform. These variants of the Hausdorff–Young theorem appear difficult to find in the literature. We conclude the paper with an example related to an open problem.

中文翻译：

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关于Laplace-Carleson嵌入和Fourier变换的$ L ^ p $映射属性

我们研究大指数的所谓Laplace-Carleson嵌入。特别是，我们扩展了Jacob，Partington和Pott的一些结果。我们还将讨论Sobolev–和Besov空间的一些相关结果，以及Fourier变换的映射属性。Hausdorff-Young定理的这些变体在文献中似乎很难找到。我们以与开放问题相关的示例作为本文的结尾。