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\(L^ p\) bounds for spectral multipliers on nilpotent groups. (English) Zbl 0739.42010

For a class of spectral multiplier operators associated to left-invariant homogeneous subelliptic second-order differential operators on nilpotent Lie groups, a criterion of Hörmander type for the \(L^ p\)-and weak type (1,1)-boundedness is given. The order of differentiability required is half the homogeneous dimension of the group.

MSC:

42B15 Multipliers for harmonic analysis in several variables
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
35P99 Spectral theory and eigenvalue problems for partial differential equations
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