Asymmetric Affine Moser -
نویسنده
چکیده
As a follow-up of Haberl-Schuster’s “Asymmetric affine Lp Sobolev inequalities” and Cianchi-Lutwak-Yang-Zhang’s “Affine Moser-Trudinger and Morrey-Sobolev inequalities”, we establish sharp Moser-Trudinger and MorrySobolev inequalities induced by the positive part of a directional derivative on the unit Euclidean sphere. 1. Theorem In their 2009 JFA paper [1], Haberl-Schuster prove the following asymmetric affine Lp Sobolev inequality: Theorem 1. [1, Theorem 1] If f ∈W (R) with 1 ≤ p < n, then (1) αn,p‖f‖ np n−p ≤ ( ∫ Sn−1 ‖D v f‖ −n p dv )− 1 n , where
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