A Kind of Estimate of Difference Norms in Anisotropic Weighted Sobolev-Lorentz Spaces. (4th August 2009) - Chen, Jiecheng; Li, Hongliang
Abstract : We investigate the functions spaces onℝ n for which the generalized partial derivativesD k r k f exist and belong to different Lorentz spacesΛ p k, s k ( w ), wherep k > 1 andw is nonincreasing and satisfies some special conditions. For the functions in these weighted Sobolev-Lorentz spaces, the estimates of the Besov type norms are found. The methods used in the paper are based on some estimates of nonincreasing rearrangements and the application ofB p, B p, ∞ weights.