4 problems

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Open problem on entropy numbers of integral-operator classes
Open problem 1. For large enough $r$ , prove
Problemopenentropy-numbers function-classes integral-operatorsarXiv posted 2 days ago
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Conjecture on entropy numbers of mixed smoothness classes in the uniform norm
Let $\mathbf W^r_{q,\alpha}$ denote the mixed smoothness function class on the $d$ -dimensional domain, and let $\varepsilon_k(\mathbf W^r_{q,\alpha},L_\infty)$ be its $k$ th entropy…
Conjectureopenapproximation-theory entropy-numbers mixed-smoothnessarXiv posted 2 days ago
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Conjecture on entropy numbers of absolutely convex hulls in the critical Lorentz case
Entropy-hull conjecture. Then
Conjectureopenconvex-hulls entropy-numbers lorentz-spacesarXiv posted 2 days ago
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The critical-case entropy conjecture for weighted summation operators on trees
Critical-case entropy conjecture. The logarithmic factor is unnecessary; that is,
Conjectureopenentropy-numbers trees weighted-operatorsarXiv posted 2 days ago

Open problem on entropy numbers of integral-operator classes