Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and Lp-Lq Fourier multipliers on compact homogeneous manifolds

2015/04/27 by Rauan Akylzhanov, Akylzhanov, Rauan, Ерлан Нурсултанов +3 · 1 citation
Mathematics · #22D25 #22E30 (Secondary) #43A15 #43A22 (Primary) #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1504.07043

openalex publication_date 2015/04/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we prove new inequalities describing the relationship between the "size" of a function on a compact homogeneous manifold and the "size" of its Fourier coefficients. These inequalities can be viewed as noncommutative versions of the Hardy-Littlewood inequalities obtained by Hardy and Littlewood on the circle. For the example case of the group SU(2) we show that the obtained Hardy-Littlewood inequalities are sharp, yielding a criterion for a function to be in L^p on SU(2) in terms of its Fourier coefficients. We also establish Paley and Hausdorff-Young-Paley inequalities on general compact homogeneous manifolds. The latter is applied to obtain conditions for the L^p-L^q boundedness of Fourier multipliers for 1

Citations

• Hardy-Littlewood inequalities and Fourier multipliers on SU(2)
• Estimates for translation invariant operators in Lp spaces
• The Multiplier Problem for the Ball

Cited by

• Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses

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