## Abstract We investigate the spaces of functions on β^__n__^ for which the generalized partial derivatives __D____~k~f__ exist and belong to different Lorentz spaces __L__ . For the functions in these spaces, the sharp estimates of the Besov type norms are found. The methods used in the paper are
β¦ LIBER β¦
Estimates for Sobolev norms of triangular mappings
β Scribed by R. I. Zhdanov; Yu. V. Ovsienko
- Book ID
- 111494929
- Publisher
- Allerton Press Inc
- Year
- 2007
- Tongue
- English
- Weight
- 197 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0027-1322
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We give a new proof of the following inequality. In any dimension n G 2 and for Ε½ . 1-p-nlet s s n q p r2 p. Then p, s Ε½ n . where L R denotes the usual Sobolev space and ΩΒ¨denotes the gradient of The choice of s is optimal, as is the requirement that n ) p. In addition, some Sobolev norms of u ΩΒ¨