Extremizers for Adjoint Restriction to Pairs of Translated Paraboloids

Abstract

Consider the adjoint restriction inequality associated with the hypersurface $\{(\tau ,\xi )\in {\mathbb{R}}^{d+1}:\tau =|\xi {|}^2\}\cup \{(\tau ,\xi )\in {\mathbb{R}}^{d+1}:\tau -{\tau }_0=|\xi -{\xi }_0{|}^2\}$ for any $({\tau }_0,{\xi }_0)\ne 0$. We prove that extremizers do not exist for this inequality and fully characterize extremizing sequences in terms of extremizers for the adjoint restriction inequality for the paraboloid.

References in corpus (1)

• Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation

Cited by in corpus (1)

• On profile decomposition for Airy type equation