## Abstract The paper deals with sharp embeddings of the spaces __B__ and __F__ into rearrangement‐variant spaces and related Hardy inequalities. Here (1/~p~, __s__) belongs to the interior of the shaded invariant spaces region in the Figure
On Critical Cases of Sobolev′s Inequalities
✍ Scribed by T. Ozawa
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 312 KB
- Volume
- 127
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
We present a new form of the Trudinger-type inequality, which shows an explicit dependence. Moreover, we give an alternative proof of the Brezis-GallouetWainger inequality. 1995 Academic Press, Inc.
📜 SIMILAR VOLUMES
Let (M, g) be a smooth compact Riemannian N-manifold, N 2, let p # (1, N) real, and let H p 1 (M) be the Sobolev space of order p involving first derivatives of the functions. By the Sobolev embedding theorem, H p 1 (M)/L p\* (M) where p\*=NpÂ(N& p). Classically, this leads to some Sobolev inequalit
## Abstract The best constant in a generalized complex Clarkson inequality is __C__~__p,q__~ (ℂ) = max {2^1–1/__p__^ , 2^1/__q__^ , 2^1/__q__ –1/__p__ +1/2^} which differs moderately from the best constant in the real case __C__~__p,q__~ (ℝ) = max {2^1–1/__p__^ , 2^1/__q__^ ,__B__~__p,q__~ }, where