We give a new proof of the following inequality. In any dimension n G 2 and for Ž . 1-p-nlet s s n q p r2 p. Then p, s Ž n . where L R denotes the usual Sobolev space and ٌ¨denotes the gradient of The choice of s is optimal, as is the requirement that n ) p. In addition, some Sobolev norms of u ٌ¨
Estimates of the Sobolev Norm of a Product of Two Functions
✍ Scribed by Josip Tambača
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 94 KB
- Volume
- 255
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
In this paper we estimate the Sobolev norm of a product of two scalar functions. The proof is direct and it follows by use of the Littlewood᎐Paley theory.
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