On a class of interpolation inequalities on the 2D sphere

S. V. Zelik   ; A. A. Ilyin

Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 396-410

Résumé

We prove estimates for the $L^p$-norms of systems of functions and divergence-free vector functions that are orthonormal in the Sobolev space $H^1$ on the 2D sphere. As a corollary, order sharp constants for the embedding $H^1\hookrightarrow L^q$, $q<\infty$, are obtained in the Gagliardo-Nirenberg interpolation inequalities. Bibliography: 25 titles.

Détail

Keywords: Gagliardo-Nirenberg inequalities, sphere, orthonormal systems.

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