论文标题
强硬木不平等和$ l^p $ - $ l^q $ fourier乘数紧凑型超组
Hardy-Littlewood inequality and $L^p$-$L^q$ Fourier multipliers on compact hypergroups
论文作者
论文摘要
本文讨论了致力于紧凑型高组上函数的范围与其傅立叶系数的规范之间的比较。我们证明了紧凑型高群的经典佩利不平等现象，这进一步使耐铁的小木和豪斯多夫·尤恩格 - 帕利（PITT）不平等在非共同环境中。我们建立了Hörmander的$ l^p $ - $ l^q $傅立叶乘数定理，$ 1 <p \ leq 2 \ leq q <\ infty $作为hausdorff-young-paley不平等的应用。我们研究了由紧凑型谎言组的结合类别和一类可计数的紧凑型超级组构建的超级组的结果。
This paper deals with the inequalities devoted to the comparison between the norm of a function on a compact hypergroup and the norm of its Fourier coefficients. We prove the classical Paley inequality in the setting of compact hypergroups which further gives the Hardy-Littlewood and Hausdorff-Young-Paley (Pitt) inequalities in the noncommutative context. We establish Hörmander's $L^p$-$L^q$ Fourier multiplier theorem on compact hypergroups for $1<p \leq 2 \leq q<\infty$ as an application of Hausdorff-Young-Paley inequality. We examine our results for the hypergroups constructed from the conjugacy classes of compact Lie groups and for a class of countable compact hypergroups.
