The Boundedness of the (Sub)Bilinear Maximal Function along "non-flat" smooth curves

2019/03/26 by Gaitan, Alejandra, Lie, Victor · 4 citations
#42A45 #42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.11002

Abstract

Let NF be the class of smooth non-flat curves near the origin and near infinity previously introduced by the second author and let γ\inNF. We show - via a unifying approach relative to the correspondent bilinear Hilbert transform H_Γ - that the (sub)bilinear maximal function along curves Γ=(t,-γ(t)) defined as M_Γ(f,g)(x):=sup_εgt;0 (1)/(2ε) ∫_-ε^ε |f(x-t) g(x+γ(t))| dt is bounded from L^p(ℝ)× L^q(ℝ)→ L^r(ℝ) for all p, q and r Hölder indices, that is (1)/(p)+(1)/(q)=(1)/(r), with 1

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