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arXiv · 1411.1254

Vector valued $q$-variation for differential operators and semigroups II

Guixiang Hong·Tao Ma
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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.

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Guixiang Hong, Tao Ma. 2014-12-06. Vector valued $q$-variation for differential operators and semigroups II. https://arxiv.org/abs/1411.1254

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