Let $U$ be an extension domain in $n$ dimensions. It is known that general Sobolev inequalities provide continuity of $W^{k,p}$ functions, provided $kp>n$. So, if one fixes $p$ (I am interested in $p=2$), one obtains that sufficiently weakly smooth functions have pointwise values.
I guess this criterion is non optimal, and one could obtain sharper results in fractional Sobolev spaces. However I could only find the same embedding with $s \in (0,1)$. So is it true that for $s>0$ generic with $sp>n$, Sobolev functions are continuous? How can one see this/where is a reference for this?
Deriving such a result from the case $s\in (0,1)$ like one derives the higher order Morrey inequalities from the counterpart with just first derivatives doesn't work here.
Thanks in advance!