Lp-boundedness of the Hilbert transform and maximal function along flat curves in ℝn
نویسندگان
چکیده
منابع مشابه
On the Boundedness of the Bilinear Hilbert Transform along “non-flat” Smooth Curves
We are proving L(R) × L(R) → L(R) bounds for the bilinear Hilbert transform HΓ along curves Γ = (t,−γ(t)) with γ being a smooth “non-flat” curve near zero and infinity.
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The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of disciplines; this includes problems in Fourier convergence, complex analysis, potential theory, modulatio...
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The purpose of this paper is to prove the L p (R n ; dd) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dd = e ?jxj 2 dx. Let dd = e ?jxj 2 dx be a Gaussian measure in Euclidean space R n. We consider the non-centered maximal function deened by Mf(x) = sup x2B 1 (B) Z B jfj dd; where the supremum is taken over all balls B in R ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1995
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1995.168.383