On the Moser–Trudinger inequality in fractional Sobolev–Slobodeckij spaces
On the Moser–Trudinger inequality in fractional Sobolev–Slobodeckij spaces
We give a contribution to the problem of finding the optimal exponent in the Moser–Trudinger inequality in the fractional Sobolev–Slobodeckij space \widetilde{W}^{s,p}_0(\Omega) , where \Omega \subset \mathbb R^N is a bounded domain, s \in (0,1) , and sp = N . We exhibit an explicit exponent \alpha^*_{s,N}>0 , which does …