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Category Archives: Functional inequalities
Weighted Moser-Trudinger inequalities
Recently, M. Ishiwata, M. Nakamura and H. Wadade (see this link) proved the following weighted Moser–Trudinger inequalities of the scaling invariant form in whole space (1) for any radial function with and for any where is the surface … Continue reading
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Tagged Weighted Moser-Trudinger inequality
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Hardy-Rellich inequality on functions which are orthogonal to radial functions.
Hardy inequality asserts that for any function . Rellich inequality asserts that for any function . The constants and are sharp. In this post, we will improve these inequalities when restricting to the functions which is orthogonal to all radial function, … Continue reading
Manifolds with nonnegative Ricci curvature and Sobolev inequalities
The main object of this post is the following nice result due to Michel Ledoux: Let be a complete dimensional Riemannian manifold with nonnegative Ricci curvature. If the following Sobolev inequality for some with and is the best constant in … Continue reading
An improved Poincaré inequality for Gaussian measure.
Let denote standard Gaussian measure on , i. e The Poincaré inequality for states that for any Lipschitz function in , it holds This inequality is sharp and equality holds iff for some vector and . An improvement of Poincaré … Continue reading
Nguyễn Văn Hoàng 