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These are the notes of a lecture given at the university of Wroclaw in 1996.We present results of semigroups of (sub)positive contractions on L^p-spaces.The dilation theorem of Akcoglue and sucheston is considered as a startingpoint. We construct a dilation of a strongly continuous semigroup of(sub)positive contractions on L^p-space, 1<p<infinity by a strongly continuousgroup of invertible isometries acting on some larger L^p-space. Thetransference results, for functions of the generators, are established as wellas some square and maximal functions. This applies especially to sub-markoviansemigroups.

N Dilations and Transference for Continuous One-Parameter Semigroups of Positive Contractions on $\mathcal{L}^p$-spaces