Embeddings of function spaces: a criterion in terms of differences

作者：Haroske Dorothee D^*; Triebel Hans

来源：Complex Variables and Elliptic Equations, 2011, 56(10-11): 931-944.

DOI：10.1080/17476933.2010.551203

• Besov spaces
• Sobolev spaces
• embeddings
• differences
• modulus of smoothness

We study criteria for the embedding B-p,q(s)(R-n) -> L-r(R-n), 0 < p, q <= infinity, 1 < r < infinity, s > 0 with s - n/p = -n/r, in terms of inequalities for iterated differences and moduli of smoothness. The article was inspired by the recent paper by W. Trebels [W. Trebels, Inequalities for moduli of smoothness versus embeddings of function spaces, Arch. Math. 94 (2010), pp. 155-164], although we deal with the inhomogeneous setting here. Another motivation came from the new characterization of Sobolev spaces by H. Triebel [H. Triebel, Sobolev-Besov spaces of measurable functions, Studia Math. 201(1) (2010), pp. 69-86]. We also collect some consequences formulated in the spirit of inequalities of Ul'yanov type. In the end an interesting decomposition technique is presented.

• 出版日期2011