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Weak Type (1,1) Bounds for Some Operators Related to the Laplacian with Drift on Real Hyperbolic Spaces

H. Q. Li ; Peter Sjögren (Institutionen för matematiska vetenskaper)
Potential Analysis (0926-2601). Vol. 46 (2017), 3, p. 463-484.
[Artikel, refereegranskad vetenskaplig]

The setting of this work is the n-dimensional hyperbolic space , where the Laplacian is given a drift in the direction. We consider the operators defined by the horizontal Littlewood-Paley-Stein functions for the heat semigroup and the Poisson semigroup, and also the Riesz transforms of order 1 and 2. These operators are known to be bounded on , for the relevant measure. We show that most of the Littlewood-Paley-Stein operators and all the Riesz transforms are also of weak type (1,1). But in some exceptional cases, we disprove the weak type (1,1).

Nyckelord: Littlewood-Paley-Stein function, Riesz transform, Laplacian with drift, Real hyperbolic space

Denna post skapades 2017-05-09.
CPL Pubid: 249195


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