Theorems of imbedding Besov spaces into ideal spaces

Yu. V. Netrusov

Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 69-82

Résumé

The paper examines imbeddings of Besov spaces $B^\omega_{E,\theta}$ in ideal spaces (Banach lattices) given that $\omega\in S_{k_\omega}$). In particular, the symmetric hull of the space $B^\omega_{E,\theta}$ is described ($E$ is a symmetric space), an inequality of different metrics is obtained, and imbeddings in Orlicz and Lorentz spaces and in some weighted spaces are studied. Most of the results are easily extended to the anisotropic case.