Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4619217 | Journal of Mathematical Analysis and Applications | 2010 | 11 Pages |
Abstract
We consider a triple of N-functions (M,H,J) that satisfy the Îâ²-condition, μ=|x|αdx and suppose that an additive variant of interpolation inequality holdsâ«RnM(|âu|)μ(dx)⩽C(â«RnH(|u|)μ(dx)+â«RnJ(|â(2)u|)μ(dx)), where uâRâWloc2,1(Rn), R is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions â«RnH(|u|)μ(dx) and â«RnJ(|â(2)u|)μ(dx). Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Agnieszka KaÅamajska, Miroslav Krbec,