Geodesic
On a~class of interpolation inequalities on the 2D sphere
Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 396-410

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Gagliardo-Nirenberg inequalities, sphere, orthonormal systems. 
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     title = {On a~class of interpolation inequalities on the {2D} sphere},
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S. V. Zelik; A. A. Ilyin. On a~class of interpolation inequalities on the 2D sphere. Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 396-410. http://geodesic.mathdoc.fr/item/SM_2023_214_3_a5/