2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65883We prove that if a function $f \in L^p({\Bbb {R}} ^d)$ has vanishing periodizations then $\|f\|_{p'} \lesssim \|f\|_{p}$, provided $1 \le p < \frac {2d}{d + 2}$ and dimension $d \ge 3$.Classical Analysis and ODEs42text