Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 923-940, 2011

# Compact embeddings of Besov spaces involving only slowly varying smoothness

## Antonio Caetano, Amiran Gogatishvili, Bohumír Opic

António Caetano, Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal e-mail: acaetano@ua.pt (corresponding author); Amiran Gogatishvili, Institute of Mathematics, Academy of Sciences of the Czech Republic, ®itná 25, 115 67 Prague 1, Czech Republic e-mail: gogatish@math.cas.cz; Bohumír Opic, Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic e-mail: opic@karlin.mff.cuni.cz

Abstract: We characterize compact embeddings of Besov spaces $B^{0,b}_{p,r}(\mathbb{R}^n)$ involving the zero classical smoothness and a slowly varying smoothness $b$ into Lorentz-Karamata spaces $L_{p, q; \bar{b}}(\Omega)$, where $\Omega$ is a bounded domain in $\mathbb{R}^n$ and $\bar{b}$ is another slowly varying function.

Keywords: Besov spaces with generalized smoothness, Lorentz-Karamata spaces, compact embeddings

Classification (MSC 2010): 46E35, 46E30

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