2 9 A pr 2 00 8 SPACES H 1 AND BMO ON ax + b – GROUPS
نویسندگان
چکیده
Abstract. Let S be the group R ⋉ R endowed with the Riemannian symmetric space metric d 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 space H 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 H. We then prove that singular integral operators whose kernels satisfy a suitable integral Hörmander condition are bounded from H to L and from L∞ to BMO. We also study the real interpolation between H, BMO and the L spaces.
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