Multivariate H "ormander-type multiplier theorem for the Hankel\n transform

2011/10/11 by Jacek Dziubański, Dziubański, Jacek, Marcin Preisner +3
Mathematics · #42B15 (Primary) 33C10 #42B20 #42B30 (Secondary) #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1110.2348

openalex publication_date 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H(f)(x)=\∫_(0,infty)^d f(v) E_x(v) d\ν(v), be the multivariable\nHankel transform, where E_x(v)=\∏_k=1^d (x_k v_k)^-a_k+1/2\nJ_ak-1/2(x_k v_k), d\ν(v)=v^a dv, a=(a₁,...,a_d). We give sufficient\nconditions on a bounded continuous function m(v) which guarantee that the\noperator H(m Hf) is bounded on L^p(d\ν) and of weak-type (1,1), or bounded on\nthe Hardy space H¹((0,infty)^d, d\ν) in the sense of Coifman-Weiss.\n

Citations

• Algebras of differential operators on Lie groups and spectral multipliers

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