Endpoint uniform Sobolev inequalities for elliptic operators with applications

Shanlin Huang,Quan Zheng

doi:10.1016/j.jde.2019.05.005

Endpoint uniform Sobolev inequalities for elliptic operators with applications

Shanlin Huang, Quan Zheng

Open Access

https://doi.org/10.1016/j.jde.2019.05.005

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Journal: Journal of Differential Equations	Publication Date: May 10, 2019
Citations: 7	License type: publisher-specific-oa

Affiliation: Huazhong University of Science and Technology

#Certain Class Of Potentials #Elliptic Operators + Show 6 more

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Abstract

In this paper, we obtain sharp restricted weak-type uniform Sobolev inequalities for a class of elliptic operators P(D). In particular, we improve a recent result of Sikora, Yan and Yao [24] to the endpoint case. The sharpness is proved by constructing explicit counterexamples. As applications, we establish Stein-Tomas type inequalities for H=P(D)+V with certain class of potentials V.

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