Geodesic
Reduced Sobolev Inequalities
Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 159-167

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The Sobolev inequality of order m asserts that if p ≧ 1, mp < n and 1/q = 1/p — m/n, then the Lq-norm of a smooth function with compact support in Rn is bounded by a constant times the sum of the Lp -norms of the partial derivatives of order m of that function. In this paper we show that that sum may be reduced to include only the completely mixed partial derivatives or order m, and in some circumstances even fewer partial derivatives.
DOI : 10.4153/CMB-1988-024-1
Mots-clés : 46E35 
Adams, R. A. Reduced Sobolev Inequalities. Canadian mathematical bulletin, Tome 31 (1988) no. 2, pp. 159-167. doi: 10.4153/CMB-1988-024-1
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     title = {Reduced {Sobolev} {Inequalities}},
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     year = {1988},
     volume = {31},
     number = {2},
     doi = {10.4153/CMB-1988-024-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-024-1/}
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