The Walsh model for $M_2^*$ Carleson
@article{Demeter2007TheWM, title={The Walsh model for \$M\_2^*\$ Carleson}, author={Ciprian Demeter and Michael T. Lacey and Terence Tao and Christoph Thiele}, journal={Revista Matematica Iberoamericana}, year={2007}, volume={24}, pages={721-744} }
We study the Walsh model of a certain maximal truncation of Carleson's operator, related to the Return Times Theorem from Ergodic Theory.
5 Citations
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References
SHOWING 1-8 OF 8 REFERENCES
Lp estimates for the biest I. The Walsh case
- Mathematics
- 2001
Abstract.We prove Lp estimates (Theorem 1.8) for the Walsh model of the ‘‘biest’’, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in…
Breaking the duality in the return times theorem
- Mathematics
- 2006
We prove Bourgain's Return Times Theorem for a range of exponents $p$ and $q$ that are outside the duality range. An oscillation result is used to prove hitherto unknown almost everywhere convergence…
On the bilinear Hilbert transform.
- Mathematics
- 1998
In joint work with C. Thiele, the author has shown that A. Calderón’s bilinear Hilbert transform extends to a bounded operator on certain products of L spaces. This article illustrates the method of…
Pointwise ergodic theorems for arithmetic sets
- Mathematics
- 1989
converge almost surely for N -+ co, assuming f a function of class L~(~, ~). Here and in the sequel, one denotcs by ~ a probability measure and by T a measure-preserving automorphism. The natural…
The quartile operator and pointwise convergence of Walsh series
- Mathematics
- 2000
The bilinear Hilbert transform is given by H(f, g)(x) := p.v. ∫ f(x− t)g(x + t) t . It satisfies estimates of the type ‖H(f, g)‖r ≤ C(s, t)‖f‖s‖g‖t. In this paper we prove such estimates for a…
Appendix on return-time sequences
- Mathematics
- 1989
© Publications mathématiques de l’I.H.É.S., 1989, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
Return times in dynamical systems
- Philosophy
- 2005
Dans cette these, deux aspects asymptotiques des temps de retour et d'entree sont etudies: les taux locaux de temps de retour, et les lois limites des k-iemes temps de retour et d'entree. Dans le…