We present conditions which are necessary and sufficient for compact embeddings of Bessel potential spaces H_σ_X(ℝ_n_), modelled upon a rearrangement-invariant Banach function spaces X(ℝ_n_), into generalized Hölder spaces involving k-modulus of smoothness. To this end, we derive a characterization of compact subsets of generalized Hölder spaces. We apply our results to the case when X(ℝ_n_) is a Lorentz–Karamata space Lp,q;b(ℝ_n_). Applications cover both superlimiting and limiting cases.
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Amiran Gogatishvili, Júlio S. Neves, Bohumír Opic, Compact Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving <i>k</i>-Modulus of Smoothness. Z. Anal. Anwend. 30 (2011), no. 1, pp. 1–27DOI 10.4171/ZAA/1421