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Some logarithmic function spaces, entropy numbers, applications to spectral theory

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Haroske D.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction.........................................................................................5 1. Non-limiting embeddings - a short review........................................8 2. The spaces Lₚ(log L)ₐ on ℝⁿ.........................................................12 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

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1 Haroske D.

1 1998

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Some logarithmic function spaces, entropy numbers, applications to spectral theory