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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn072, 9 pages, doi:10.1093/imrn/rnn072 published on July 12, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

A Theorem about Three Quadratic Forms

Oliver Dragicevic1, Sergei Treil2 and Alexander Volberg3

1 Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
2 Department of Mathematics, Brown University, 151 Thayer Street, Box 1917, Providence, RI 02912, USA
3 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA and School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK

Correspondence: Correspondence to be sent to: oliver.dragicevic{at}fmf.uni-lj.si

We prove a self-improvement property regarding quadratic forms on arbitrary vector spaces. We discuss several consequences of this result, in particular those concerning dimension-free Lp estimates of certain singular integral operators (Riesz transforms).


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