Journal of Inequalities and Applications
Volume 2 (1998), Issue 3, Pages 229-233
On an inequality conjectured by T.J. Lyons
Department of Mathematics, The University of Melbourne, Parkville 3052, Victoria, Australia
Received 1 April 1997
Copyright © 1998 E. R. Love. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be any positive integer, and any positive real numbers. The inequality
was conjectured for by T.J. Lyons, after he had proved it with an extra factor on the right, in a preprint (Imperial College of Science, Technology and Medicine, 1995). Many numerical trials confirmed the conjecture, and none disproved it. The present paper proves it, with strict inequality, for all a in sufficiently small neighbourhoods of