Pointwise convergence of the ergodic bilinear Hilbert transform
نویسندگان
چکیده
منابع مشابه
Pointwise Convergence of the Ergodic Bilinear Hilbert Transform
Let X = (X,Σ,m, τ) be a dynamical system. We prove that the bilinear series ∑ ′N n=−N f(τnx)g(τ−nx) n converges almost everywhere for each f, g ∈ L(X). We also give a proof along the same lines of Bourgain’s analog result for averages.
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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 proof by giving a complete proof of an inequality which is slightly weaker than the original conjecture of Calderón concerning this transform. 1991 Mathematics Subject Classification: 42A50
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2007
ISSN: 0019-2082
DOI: 10.1215/ijm/1258138536