The non-resonant bilinear Hilbert--Carleson operator
Résumé
In this paper we introduce the class of bilinear Hilbert--Carleson operators $\{BC^a\}_{a>0}$ defined by $$ BC^{a}(f,g)(x):= \sup_{\lambda\in {\mathbb R}} \Big|\int f(x-t)\, g(x+t)\, e^{i\lambda t^a} \, \frac{dt}{t} \Big| $$ and show that in the non-resonant case $a\in (0,\infty)\setminus\{1,2\}$ the operator $BC^a$ extends continuously from $L^p({\mathbb R})\times L^q({\mathbb R})$ into $L^r({\mathbb R})$ whenever $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$ with $1
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https://hal.science/hal-03452471
Soumis le : vendredi 26 novembre 2021-22:53:07
Dernière modification le : vendredi 29 mars 2024-10:34:33
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Cristina Benea, Frederic Bernicot, Victor Lie, Marco Vitturi. The non-resonant bilinear Hilbert--Carleson operator. 2021. ⟨hal-03452471⟩
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