Sobolev inequality $\|u\|_{L^{2p}}\le C\,\|u\|_{W^{1,p}}$ on the cylinder $\mathbb R\times S^1$

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Sobolev inequality $\|u\|_{L^{2p}}\le C\,\|u\|_{W^{1,p}}$ on the cylinder $\mathbb R\times S^1$ · Prove2Me