I want to show that for $s\in[0,n/2)$ and $p \in [2,2n/(n-2s))$ we have the following (continuous) inclusion $$ H^s(\mathbb{R}^n) \subset L^p(\mathbb{R}^n). $$
I have tried to find two interpolation pairs between Sobolev and $L^p$ spaces using Riesz-Thorin and interpolation theorem for sobolev spaces, but nothing has worked out. Maybe I am not using the right coefficients. Any hint or reference would be very appreciated!
Edit: I have proven the fact that Sobolev space of a certain rank can be embedded into $C_0^N$ (for some N). To use interpolation results I need now that $H^{n/2} \subset L^q$ for $0<q<2n/(n-2s)$.