Dear mathoverflowers,

I would like to have a reference regarding the optimal constant in the Sobolev embedding

$$ \|u\|_{L^q}\leq C_{s,q}\|u\|_{\dot{H}^s}, $$

($H^s$ denotes the standard L^2 Sobolev space $W^{s,2}$)

for zero mean periodic functions. Can you help me? Thank you in advance.

PD: A reference on the slightly different embedding

$$ \|u\|_{L^q}\leq C_{s,q}\|u\|_{H^s} $$

is also appreciated :-).



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