Vector valued -variation for differential operators and semigroups II
arXiv:1411.1254
Abstract
In this paper, we establish UMD lattice-valued variational inequalities for differential operators, ergodic averages and analytic semigroups. These results generalize, on the one hand some scalar-valued variational inequalities in ergodic theory, on the other hand Xu's very recent result on UMD lattice-valued maximal inequality. As a consequence, we deduce the jump estimates and obtain quantitative information on the rate of the pointwise convergence.
18 pages. Significant changes on the presentation but with the main results being kept to avoid arXiv admin note