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Littlewood-Paley-Stein theory on \({\mathbb{C}}^ n\) and Weyl multipliers. (English) Zbl 0734.42010

The author develops a Littlewood-Paley-Stein theory suitable for certain semi-groups that arise naturally in the study of the Weyl transform on \({\mathbb{C}}^ n\). A principal tool in the study is the Ricci-Stein theory of oscillatory integrals.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
44A15 Special integral transforms (Legendre, Hilbert, etc.)
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B15 Multipliers for harmonic analysis in several variables
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
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