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Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrödinger operators. (English) Zbl 1214.46019

On a space of homogeneous type in the sense of Coifman and Weiss, the authors define and analyse localized Morrey-Campanato and Morrey-Campanato-BLO spaces. They prove the boundedness of radial and Poisson maximal functions between these spaces, as well as the boundedness of the Littlewood-Paley \(g\)-function. These results are then applied to prove estimates on the one-parameter semigroups generated by (possibly degenerate) Schrödinger operators on \(\mathbb{R}^d\), on Heisenberg groups, and on connected and simply connected nilpotent Lie groups.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
35J10 Schrödinger operator, Schrödinger equation
47D06 One-parameter semigroups and linear evolution equations
42B25 Maximal functions, Littlewood-Paley theory
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References:

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