Fractional Sobolev, Moser–Trudinger, Morrey–Sobolev inequalities under Lorentz norms

Abstract

We consider the Sobolev type inequalities under Lorentz norms on bounded open domains for fractional derivatives (−∆)s/2 in the following three cases: n > ps, n = ps, and n < ps, whence establishing the weak type Sobolev inequalities, Moser–Trudinger and Morrey–Sobolev inequalities for fractional derivatives in Lorentz norms. Applying these inequalities, we obtain the trace forms of six related functional inequalities. Bibliography: 44 titles.