Weak poincare inequalities, decay of Markov semigroups and concentration of measures

摘要

For a reasonable class of weak Poincare inequalities, the decay of the corresponding Markov semigroups obtained earlier by Rockner and the first named author is improved by removing an extra L-2-norm. Next, a concentration estimate of the reference measure is presented for the weak Poincare inequality, which is sharp as illustrated by some examples of one-dimensional diffusion processes.