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Yang, Dachun; Yang, Dongyong; Zhou, Yuan

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

Nagoya Math. J. 198, 77-119 (2010).
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.
Reviewer: Nils Ackermann (Mexico City)

Cited in 51 Documents

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

Keywords:

spaces of homogeneous type; maximal function; Schrödinger operator; localized Morrey-Campanato space; operator semigroup
PDFBibTeX XMLCite
\textit{D. Yang} et al., Nagoya Math. J. 198, 77--119 (2010; Zbl 1214.46019)
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References:

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