Multiple vector-valued, mixed norm estimates for Littlewood-Paley square functions

Cristina Benea, Camil Muscalu

We prove that for any $L^Q$-valued Schwartz function $f$ defined on ${\mathbb{R}}^d$, one has the multiple vector-valued, mixed norm estimate $$ \| f \|_{L^P(L^Q)} \lesssim \| S f \|…