Estimates of functions with vanishing periodizations

Details Estimates of functions with vanishing periodizations Estimates of functions with vanishing periodizations

2002-12-04

arxiv.org/abs/math/0212060v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We 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 $d \ge 3$.

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