Regularity estimates in H\"older spaces for Schr\"odinger operators via a T1 theorem

Tao Ma; P. R. Stinga; J. L. Torrea; Chao Zhang

Regularity estimates in H\"older spaces for Schr\"odinger operators via a T1 theorem

Analysis of PDEs 2012-09-07 v2 Classical Analysis and ODEs Functional Analysis

Authors: Tao Ma , P. R. Stinga , J. L. Torrea , Chao Zhang

Abstract

We derive H\"older regularity estimates for operators associated with a time independent Schr\"odinger operator of the form $-\Delta+V$ . The results are obtained by checking a certain condition on the function $T1$ . Our general method applies to get regularity estimates for maximal operators and square functions of the heat and Poisson semigroups, for Laplace transform type multipliers and also for Riesz transforms and negative powers $(-\Delta+V)^{-\gamma/2}$ , all of them in a unified way.

Keywords

Hölder regularity Schrödinger operators T1 theorem maximal operators square functions Riesz transforms heat semigroup

Cite

@article{arxiv.1109.6156,
  title  = {Regularity estimates in H\"older spaces for Schr\"odinger operators via a T1 theorem},
  author = {Tao Ma and P. R. Stinga and J. L. Torrea and Chao Zhang},
  journal= {arXiv preprint arXiv:1109.6156},
  year   = {2012}
}

Comments

22 pages, revised version. To appear in Annali di Matematica Pura ed Applicata

Regularity estimates in H\"older spaces for Schr\"odinger operators via a T1 theorem

Abstract

Keywords

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