Multiplier conditions for Boundedness into Hardy spaces

2017/02/27 by Loukas Grafakos, Grafakos, Loukas, Shohei Nakamura +5
Mathematics · #42B15 #42B30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Applied mathematics #Calculus (dental) #Economics #FOS: Mathematics #Functional Analysis (math.FA) #Hardy space #Holomorphic and Operator Theory #Keynesian economics #Mathematical analysis #Mathematical economics #Mathematics #Multiplier (economics) #Pure mathematics #math.FA #msc:42B15 #msc:42B30

paper · pdf · doi:10.48550/arxiv.1702.08190

13 pages

arxiv created 2017/02/27 · openalex publication_date 2017/02/27 · arxiv updated 2017/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the present work, we find useful and explicit necessary and sufficient conditions for linear and multilinear multiplier operators of Coifman-Meyer type, finite sum of products of Calderón-Zygmund operators, and also of intermediate types to be bounded from a product of Lebesgue or Hardy spaces into a Hardy space. These conditions state that the symbols of the multipliers σ(ξ₁,… , ξ_m) and their derivatives vanish on the hyperplane ξ₁+⋯+ξ_m=0.

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