A Gagliardo-Nirenberg inequality for Lorentz spaces
It is given an extension of the Gagliardo-Nirenberg inequality to Lorentz spaces. The generalized derivatives are written in integral form in order to prove the continuity by way of contradiction. Also Fatou's lemma is used. Then the first part follows from the classical Gagliardo-Nirenberg inequality by taking the limit as epsilon tends to zero. The proof is completed using a diagonal process and Fatou's lemma again and the definition of the Lorentz norm.
scientific article; zbMATH DE number 5156814