Regularity properties of Schr\"odinger operators
Analysis of PDEs
2011-10-05 v2 Classical Analysis and ODEs
Functional Analysis
Abstract
Let L be a Schr\"odinger operator of the form L=-\Delta+V, where the nonnegative potential V satisfies a reverse H\"older inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted H\"older spaces. We give a pointwise description of L-H\"older spaces and provide some characterizations in terms of the growth of fractional derivatives of any order and Carleson measures. Applications to fractional powers of L and multipliers of Laplace transform type developed.
Cite
@article{arxiv.1107.0184,
title = {Regularity properties of Schr\"odinger operators},
author = {Tao Ma and P. R. Stinga and J. L. Torrea and Chao Zhang},
journal= {arXiv preprint arXiv:1107.0184},
year = {2011}
}
Comments
20 pages. To appear in Journal of Mathematical Analysis and Applications