# Constant periodic Sobolev embedding

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 :-).