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Let S be the semidirect product of R^d and R^+ endowed with the Riemanniansymmetric space metric and the right Haar measure: this is a Lie group ofexponential growth. In this paper we define an Hardy space H^1 and a BMO spacein this context. We prove that the functions in BMO satisfy the John-Nirenberginequality and that BMO may be identified with the dual space of H^1. We thenprove that singular integral operators which satisfy a suitable integralHormander condition are bounded from H^1 to L^1 and from L^{\infty} to BMO. Wealso study the real interpolation between H^1, BMO and the L^p spaces.

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