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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).



References

  1. Dragicevic O., Volberg A. Bellman functions and dimensionless estimates of Littlewood-Paley type. Journal of Operator Theory (2006) 56(1):167–98.[ISI]
  2. Dragicevic O., Volberg A. Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in Lp(C). Indiana University Mathematics Journal (2005) 54(4):971–95.[CrossRef][ISI]
  3. Dragicevic O., Volberg A. Bellman function for the estimates of Littlewood-Paley type and asymptotic estimates in the p – 1 problem. C.R. Academy of Sciences, Paris, Serie 1 (2005) 340(10):731–4.
  4. Dragicevic O., Volberg A. Bilinear embedding theorem for elliptic differential operators in divergence form with real coefficients. (2006) preprint.
  5. Dragicevic O., Volberg A. Dimension free bilinear embedding and Riesz transforms associated with Hermite operators. (2007) preprint.
  6. Duffin R. J. A minimax theory for overdamped networks. Archive for Rational Mechanics and Analysis (1955) 4:221–33.
  7. Markus A. S. Introduction to the Spectral Theory of Polynomial Operator Pencils (1988) Providence, RI: American Mathematical Society.
  8. Nazarov F., Volberg A. Heat extension of the Beurling operator and estimates for its norm. St. Petersburg Mathematics Journal (2004) 15(4):563–73.
  9. Petermichl S. The sharp dimensionless bound for the Riesz transform on weighted n-dimensional Lebesgue spaces in terms of the Poisson A2 characteristic. (2006) preprint.

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
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Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Dragicevic, O.
Right arrow Articles by Volberg, A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?