Quasi-Banach Valued Inequalities via the Helicoidal method

Cristina Benea (1) , Camil Muscalu

1 LMJL - Laboratoire de Mathématiques Jean Leray

We extend the helicoidal method that we previously developed to the quasi-Banach context, proving in this way multiple Banach and quasi-Banach vector-valued inequalities for paraproducts $\Pi$ and for the bilinear Hilbert transform $BHT$. As an immediate application, we obtain mixed norm estimates for $\Pi \otimes \Pi$ in the whole range of Lebesgue exponents. One of the novelties in the quasi-Banach framework (that is, when $0

Domaines: Analyse classique [math.CA]

Cristina Benea, Camil Muscalu. Quasi-Banach Valued Inequalities via the Helicoidal method. 2016. ⟨hal-01402824⟩