On the Two Dimensional Bilinear Hilbert Transform Ciprian Demeter and Christoph Thiele
نویسنده
چکیده
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z actions. Our techniques combine novel one and a half dimensional phase-space analysis with more standard one dimensional theory.
منابع مشابه
ON THE TWO-DIMENSIONAL BILINEAR HILBERT TRANSFORM By CIPRIAN DEMETER and CHRISTOPH THIELE
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z2 actions. Our techniques combine novel one and a half-dimensional phase-space analysis with more standard one-dimensional theory.
متن کاملOn the Two Dimensional Bilinear Hilbert Transform
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z actions. Our techniques combine novel one and a half dimensional phase-space analysis with more standard one dimensional theory.
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CIPRIAN DEMETER, TERENCE TAO, AND CHRISTOPH THIELE Abstract. We establish multilinear L bounds for a class of maximal multilinear averages of functions on one variable, reproving and generalizing the bilinear maximal function bounds of Lacey [13]. As an application we obtain almost everywhere convergence results for these averages, and in some cases we also obtain almost everywhere convergence ...
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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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تاریخ انتشار 2008