1Dept. of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium 2Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium 3School of Mathematical Sciences, Queen Mary University, London, United Kingdom
Journal of Lie Theory, Tome 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.
1
Dept. of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
2
Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
3
School of Mathematical Sciences, Queen Mary University, London, United Kingdom
Vishvesh Kumar; Michael Ruzhansky. Hardy-Littlewood Inequality and Lp-Lq Fourier Multipliers on Compact Hypergroups. Journal of Lie Theory, Tome 32 (2022) no. 2, pp. 475-498. http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a7/
@article{JOLT_2022_32_2_a7,
author = {Vishvesh Kumar and Michael 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a7/}
}
TY - JOUR
AU - Vishvesh Kumar
AU - Michael Ruzhansky
TI - Hardy-Littlewood Inequality and Lp-Lq Fourier Multipliers on Compact Hypergroups
JO - Journal of Lie Theory
PY - 2022
SP - 475
EP - 498
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a7/
ID - JOLT_2022_32_2_a7
ER -
%0 Journal Article
%A Vishvesh Kumar
%A Michael Ruzhansky
%T Hardy-Littlewood Inequality and Lp-Lq Fourier Multipliers on Compact Hypergroups
%J Journal of Lie Theory
%D 2022
%P 475-498
%V 32
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2022_32_2_a7/
%F JOLT_2022_32_2_a7
