Journal of Lie Theory

no. 2
Hardy-Littlewood Inequality and Lp-Lq Fourier Multipliers on Compact Hypergroups
Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 475-498
This paper deals with the inequalities comparing 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 inequalities in the noncommutative context. We establish Hörmander's Lp-Lq Fourier multiplier theorem on compact hypergroups for 1 p ≤ 2 ≤ q ∞ as an application of the 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.
DOI: 10.5802/jolt.1239
Classification: 43A62, 43A22, 33C45, 43A90
Keywords: Paley inequality, Hardy-Littlewood inequality, Hausdorff-Paley inequality, compact hypergroups, conjugacy classes of compact Lie groups, Fourier multipliers, Lp-Lq boundedness, compact countable hypergroups 
@article{JOLT_2022_32_2_a7,
     author = {V. Kumar and M. Ruzhansky},
     title = {Hardy-Littlewood {Inequality} and {L\protect\textsuperscript{p}-L\protect\textsuperscript{q}} {Fourier} {Multipliers} on {Compact} {Hypergroups}},
     journal = {Journal of Lie Theory},
     pages = {475--498},
     year = {2022},
     volume = {32},
     number = {2},
     doi = {10.5802/jolt.1239},
     zbl = {1497.43007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1239/}
}
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%A M. Ruzhansky
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V. Kumar; M. Ruzhansky. Hardy-Littlewood Inequality and Lp-Lq Fourier Multipliers on Compact Hypergroups. Journal of Lie Theory, Volume 32 (2022) no. 2, pp. 475-498. doi: 10.5802/jolt.1239

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