A note on the Sobolev inequality
β Scribed by Gabriele Bianchi; Henrik Egnell
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 293 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this note, it is shown that the HardyαHilbert inequality for double series can Ε½ . be improved by introducing a proper weight function of the form rsin rp y Ε½ . 1y1rr Ε½ Ε½ . . O n rn with O n ) 0 into either of the two single summations. When r r r s 2, the classical Hilbert inequality is improved
A new proof is given of the nonuniform version of Fisher's inequality, first proved by Majumdar. The proof is ``elementary,'' in the sense of being purely combinatorial and not using ideas from linear algebra. However, no nonalgebraic proof of the n-dimensional analogue of this result (Theorem 3 her
Using only the elementary properties of lattice-ordered groups, we give a simple w x proof of the inequality of Maligranda and Orlicz 2 in full generality.
Given a finite boolean lattice L and four functions tr, fl, y, 6 of L to the nonnegative reals with oc(x)fl(y) <~ y(x v y)6(x A y) for all x, y e L. We show that Here x' denotes the complement of x and X v X' stands for {Xl v x~ I xl, x2 e X). This inequality turns out to be equivalent in a certain