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Compactness of the Hardy-Littlewood operator on some spaces of harmonic functions. (Russian, English) Zbl 1222.47048

Sib. Mat. Zh. 50, No. 1, 205-221 (2009); translation in Sib. Math. J. 50, No. 1, 167-180 (2009).
Summary: We study the compactness of the Hardy–Littlewood operator on several spaces of harmonic functions on the unit ball in \(\mathbb R^n\) such as: \(\alpha\)-Bloch, weighted Hardy, weighted Bergman, Besov, \(BMO_p\), and Dirichlet spaces.

MSC:

47B38 Linear operators on function spaces (general)
42B25 Maximal functions, Littlewood-Paley theory
46E15 Banach spaces of continuous, differentiable or analytic functions
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