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Sharp Estimates of the Sobolev Norm ofuTimes the Gradient ofv

✍ Scribed by M.T. Lacey

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
105 KB
Volume
205
Category
Article
ISSN
0022-247X

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✦ Synopsis

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 ٌ¨can be estimated.

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✍ Josip Tambača 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 94 KB

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.