Vol. 10, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Some energy inequalities involving fractional GJMS operators

Jeffrey S. Case

Vol. 10 (2017), No. 2, 253–280

Under a spectral assumption on the Laplacian of a Poincaré–Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS operator of order 2γ (0,2) or 2γ (2,4) and the energy of the weighted conformal Laplacian or weighted Paneitz operator, respectively. This spectral assumption is necessary and sufficient for such an inequality to hold. We prove the energy inequalities by introducing conformally covariant boundary operators associated to the weighted conformal Laplacian and weighted Paneitz operator which generalize the Robin operator. As an application, we establish a new sharp weighted Sobolev trace inequality on the upper hemisphere.

fractional Laplacian, fractional GJMS operator, Poincaré–Einstein manifold, Robin operator, smooth metric measure space
Mathematical Subject Classification 2010
Primary: 58J32
Secondary: 53A30, 58J40
Received: 6 October 2015
Revised: 6 October 2016
Accepted: 28 November 2016
Published: 23 February 2017
Jeffrey S. Case
109 McAllister Building
Penn State University
University Park, PA 16802
United States