Spaces "H^1" and "BMO" on "ax+b" - groups

Autores: Maria Vallarino
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 60, Fasc. 3, 2009, págs. 277-295
Idioma: español
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Resumen
- LetS be the group ℝ^d ⋉ ℝ^+ endowed with the Riemannian symmetric space metricd and the right Haar measure ρ The space (S, d, ρ) is a Lie group of exponential growth. In this paper we define an Hardy spaceH^1 and aBMO space in this context. We prove that the functions inBMO satisfy the John-Nirenberg inequality and thatBMO may be identified with the dual space ofH^1. We then prove that singular integral operators whose kernels satisfy a suitable integral Hörmander condition are bounded fromH^1 toL^1 and fromL^∞ toBMO. We also study the real interpolation betweenH1,BMO and theL^p spaces.