# Agenda de l’IDP

Classical functions spaces on Rd like Sobolev, Triebel-Lizorkin or Hardy spaces can be defined by means of the heat semigroup {Ht}{t>0}, where H_tf(x)=\int_{\mathbb R^d} (4\pi t)^{-d\slash 2} e^{-|x-y|^2\slash4t} f(y)\, dy. One possible definition of the real Hardy space Hp could be expressed as follows: a distribution f is an element of the Hardy space Hp(Rd), 0 < p<&infty;, if the maximal function (\star)\hfill \mathcal M_{\Delta} f(x)=\sup_{t>0}|H_tf(x)| belongs to Lp(Rd). The following natural question could be risen: {\it What could be said about the Hardy space if we replace the heat semigroup in the definition ($\star$) by another semigroup {Tt}{t>0}, of linear operators which acts on spaces Lp(Ω) ? During the talk we shall discuss properties of Hardy spaces associated with some semigroups of linear operators.