Spaces H¹ and BMO on ax+b-groups

2008/04/29 by Maria Vallarino, Vallarino, Maria
Mathematics · #22E30 #42B20 #42B30 #46B70 #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CA #msc:22E30 #msc:42B20 #msc:42B30 #msc:46B70

paper · pdf · doi:10.48550/arxiv.0804.4615

arxiv created 2008/04/29 · openalex publication_date 2008/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be the semidirect product of R^d and R⁺ endowed with the Riemannian symmetric space metric and the right Haar measure: this is a Lie group of exponential growth. In this paper we define an Hardy space H¹ and a BMO space in this context. We prove that the functions in BMO satisfy the John-Nirenberg inequality and that BMO may be identified with the dual space of H¹. We then prove that singular integral operators which satisfy a suitable integral Hormander condition are bounded from H¹ to L¹ and from L^∞ to BMO. We also study the real interpolation between H¹, BMO and the L^p spaces.

Citations

• Hp spaces of several variables

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