Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift. (19th February 2017)

• Record Type: Journal Article
• Authors: Hou, Yuexia; Niu, Pengcheng
• Other Names: Lu Guozhen Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-02-19
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/2805457
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Suppose that X 0, X 1, …, X m are left invariant real vector fields on the homogeneous group G with X 0 being homogeneous of degree two and X 1, …, X m homogeneous of degree one. In the paper we study the hypoelliptic operator with drift of the kind L = ∑ i, j = 1 m a i j X i X j + a 0 X 0, where a 0 ≠ 0 and ( a i j ) is a constant matrix satisfying the elliptic condition on R m . By proving the boundedness of two integral operators on the Morrey spaces with two weights, we obtain global Hölder estimates for L .