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Estimates of functions with vanishing periodizations

O. Kovrizhkin
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Abstract

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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O. Kovrizhkin. 2002-12-04. Estimates of functions with vanishing periodizations. https://arxiv.org/abs/math/0212060

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