Abstract and Applied Analysis

High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential

Pengcheng Niu and Kelei Zhang

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Abstract

Let { X 1 , X 2 , , X m } be the basis of space of horizontal vector fields in a Carnot group G = ( R n ; )  ( m < n ) . We prove high order Fefferman-Phong type inequalities in G . As applications, we derive a priori L p ( G ) estimates for the nondivergence degenerate elliptic operators L = - i , j = 1 m a i j ( x ) X i X j + V ( x ) with V M O coefficients and a potential V belonging to an appropriate Stummel type class introduced in this paper. Some of our results are also new even for the usual Euclidean space.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 274859, 8 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049863

Digital Object Identifier
doi:10.1155/2014/274859

Mathematical Reviews number (MathSciNet)
MR3280862

Zentralblatt MATH identifier
07022067

Citation

Niu, Pengcheng; Zhang, Kelei. High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential. Abstr. Appl. Anal. 2014 (2014), Article ID 274859, 8 pages. doi:10.1155/2014/274859. https://projecteuclid.org/euclid.aaa/1425049863


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