Improved heat kernel bounds for certain magnetic Schrödinger operators

Bui, The Anh; Ly, Fu Ken

doi:10.1090/proc/14845

Improved heat kernel bounds for certain magnetic Schrödinger operators
HTML articles powered by AMS MathViewer

by The Anh Bui and Fu Ken Ly

Proc. Amer. Math. Soc. 148 (2020), 1671-1677

DOI: https://doi.org/10.1090/proc/14845

Published electronically: January 13, 2020

PDF | Request permission

Abstract:

We obtain an improved heat kernel bound for certain magnetic Schrödinger operators. The proof utilises an improved Fefferman–Phong inequality for magnetic operators and subsolution estimates for the corresponding parabolic equations.

References

Besma Ben Ali, Maximal inequalities and Riesz transform estimates on $L^p$ spaces for magnetic Schrödinger operators I, J. Funct. Anal. 259 (2010), no. 7, 1631–1672. MR 2665406, DOI 10.1016/j.jfa.2009.09.003
Kazuhiro Kurata, An estimate on the heat kernel of magnetic Schrödinger operators and uniformly elliptic operators with non-negative potentials, J. London Math. Soc. (2) 62 (2000), no. 3, 885–903. MR 1794292, DOI 10.1112/S002461070000137X
Andrew Raich and Michael Tinker, Schrödinger operators with $A_\infty$ potentials, Potential Anal. 45 (2016), no. 2, 387–402. MR 3518679, DOI 10.1007/s11118-016-9556-z
Zhong Wei Shen, $L^p$ estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier (Grenoble) 45 (1995), no. 2, 513–546 (English, with English and French summaries). MR 1343560
Zhongwei Shen, Estimates in $L^p$ for magnetic Schrödinger operators, Indiana Univ. Math. J. 45 (1996), no. 3, 817–841. MR 1422108, DOI 10.1512/iumj.1996.45.1268