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  2.1. The spaces Lₚ(log L)ₐ(Ω) and $L_{p,q}(log L)ₐ(Ω)$................12   2.2. The spaces $Lₚ(log L)_{-a}(ℝⁿ)$, a > 0...................................20   2.3. The spaces Lₚ(log L)ₐ(ℝⁿ), a > 0.............................................27   2.4. Hölder inequalities...................................................................32   2.5. Examples.................................................................................35 3. Entropy numbers, limiting embeddings.........................................37 4. Applications..................................................................................47   4.1. Eigenvalue distribution............................................................47   4.2. Negative spectrum...................................................................53 5. Homogeneous spaces..................................................................55 References.......................................................................................58