IUMJ

Title: Interpolation inequalities for derivatives in Orlicz spaces

Authors: Katarzyna Pietruska-Paluba and Agnieszka Kalamajska

Issue: Volume 55 (2006), Issue 6, 1767-1790

Abstract:

We prove variants of the classical Gagliardo-Nirenberg inequalities in both additive and multiplicative forms, with Orlicz norms replacing the usual $L^{p}$ norms. The $N$-functions involved satisfy certain consistency conditions. We also prove more general interpolation inequalities for derivatives, where the Orlicz norm of $|\nabla u|$ is estimated by the Orlicz norms of expressions of the form $\Psi(|u|, |\nabla^{(2)}u|)$.