Logarithmic Sobolev Inequalities and Exponential Integrability

We prove the exponential integrability of Lipschitz functions in abstract Wiener spaces by using logarithmic Sobolev inequalities. We introduce two notions of Lipschitz continuity and apply the method of Davis and Simon [J. Funct. Anal.59 (1984), 335-395] to prove our main theorem. Moreover we give several conditions under which the function is exponentially integrable.