Pointwise convergence of the ergodic bilinear Hilbert transform

Ciprian Demeter

Type: Article

Publication Date: 2007-10-01

Citations: 25

DOI: https://doi.org/10.1215/ijm/1258138536

Abstract

We prove that the ergodic bilinear Hilbert transform converges almost everywhere for pairs of bounded functions.We also give a proof along the same lines of Bourgain's analog result for averages.

Locations

Illinois Journal of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	Pointwise convergence of the ergodic bilinear Hilbert transform	2006	Ciprian Demeter
+	On the two-dimensional bilinear Hilbert transform	2010	Ciprian Demeter Christoph Thiele
+	{Spaces of Infinite Measure and Pointwise Convergence of the Bilinear Hilbert and Ergodic Averages Defined by $L^{p}$-Isometries	2008	Earl Berkson Ciprian Demeter
+	On the two dimensional Bilinear Hilbert Transform	2008	Ciprian Demeter Christoph Thiele
+	A dominated ergodic theorem for some bilinear averages	2010	F. J. Martín-Reyes
+	Convergence of Ergodic Averages	1996	R. W. L. Jones Μáté Wierdl
+	Distributional estimates for the bilinear Hilbert transform	2006	Dmitriy Bilyk Loukas Grafakos
+	Ergodic Theorems and Averaging Operators on Measurable Functions	1973	Sanae-Inoue Itoh H. Körezlioğlu Wataru Takahashi
+	Pointwise convergence of ergodic averages along cubes	2010	Idris Assani
+	Banach functionals and ergodic theorems	1967	Yu. A. Shreider
+	Averages of functions and ergodic measures inF-spaces	1972	Jason Gait Shu-Chung Koo
+	On the homogeneous ergodic bilinear averages with $1$-bounded multiplicative weights	2020	El Houcein
+	Convergence of Averages in Ergodic Theory	2001	Sergey Butkevich
+ PDF Chat	Bilinear Hilbert Transform on Measure Spaces	2005	Óscar Blasco Marı́a J. Carro T. A. Gillespie
+	Ergodic theorems on Banach spaces and their applications	2005	和章江下
+	The ergodic theorem for a sequence of functions	1940	Philip T. Maker
+	An approach to pointwise ergodic theorems	1988	Jean Bourgain
+	Pointwise ergodic theorems in Lp spaces	1979	M. A. Akcoglu
+ PDF Chat	Pointwise Convergence of Ergodic Averages Along Hardy Field Sequences	2024	Mary O’Keeffe
+	Unconditional convergence of differences in ergodic theory	1997	Bryan R. Johnson

Works That Cite This (20)

Action	Title	Year	Authors
+ PDF Chat	Oscillation and the mean ergodic theorem for uniformly convex Banach spaces	2014	Jeremy Avigad Jason Rute
+	Variational bounds for a dyadic model of the bilinear Hilbert transform	2012	Yen Do Richard Oberlin Eyvindur A. Palsson
+	Some open problems on multiple ergodic averages	2011	Nikos Frantzikinakis
+ PDF Chat	Pointwise ergodic theorems for non-conventional bilinear polynomial averages	2022	Ben Krause Mariusz Mirek Terence Tao
+ PDF Chat	Variational bounds for a dyadic model of the bilinear Hilbert transform	2013	Yen Do Richard Oberlin Eyvindur A. Palsson
+ PDF Chat	Maximal multilinear operators	2008	Ciprian Demeter Terence Tao Christoph Thiele
+	A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages	2015	Pavel Zorin‐Kranich
+ PDF Chat	On the homogeneous ergodic bilinear averages with Möbius and Liouville weights	2020	El Houcein El Abdalaoui
+	On the two-dimensional bilinear Hilbert transform	2010	Ciprian Demeter Christoph Thiele
+	Bilinear Hilbert Transforms and (Sub)Bilinear Maximal Functions along Convex Curves	2020	Junfeng Li Haixia Yu

Works Cited by This (10)

Action	Title	Year	Authors
+	On the bilinear Hilbert transform	1998	Michael T. Lacey
+ PDF Chat	L p estimates for the biest II. The Fourier case	2004	Camil Muscalu Terence Tao Christoph Thiele
+	The Bilinear Maximal Functions Map into L p for 2/3 < p ≤ 1	2000	Michael T. Lacey
+ PDF Chat	Maximal multilinear operators	2008	Ciprian Demeter Terence Tao Christoph Thiele
+ PDF Chat	Breaking the duality in the return times theorem	2008	Ciprian Demeter Michael T. Lacey Terence Tao Christoph Thiele
+ PDF Chat	Proof of the Ergodic Theorem	1931	George D. Birkhoff
+	The bilinear Hilbert transform	2013	Camil Muscalu Wilhelm Schlag
+	The bilinear maximal functions map into L^p for 2/3 < p <= 1	2000	Michael T. Lacey
+	Double recurrence and almost sure convergence.	1990	Jean Bourgain
+	Wiener Wintner Ergodic Theorems	2003	Idris Assani