On a class of interpolation inequalities on the 2D sphere
Abstract
We prove estimates for the Lp-norms of systems of functions and divergence free vector functions that are orthonormal in the Sobolev space H1 on the 2D sphere. As a corollary, order sharp constants in the embedding H1 Lq, q<∞, are obtained in the Gagliardo--Nirenberg interpolation inequalities.
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