Embeddings of Besov spaces of logarithmic smoothness
Volume 223 / 2014
Studia Mathematica 223 (2014), 193-204
MSC: Primary 46E35; Secondary 41A65.
DOI: 10.4064/sm223-3-1
Abstract
This paper deals with Besov spaces of logarithmic smoothness $B_{p,r}^{0,b}$ formed by periodic functions. We study embeddings of $B_{p,r}^{0,b}$ into Lorentz–Zygmund spaces $L_{p,q}(\log L)_{\beta }$. Our techniques rely on the approximation structure of $B_{p,r}^{0,b}$, Nikol'skiĭ type inequalities, extrapolation properties of $L_{p,q}(\log L)_{\beta }$ and interpolation.
