Weak Type (1,1) Bounds for Some Operators Related to the Laplacian with Drift on Real Hyperbolic Spaces
Journal article, 2017

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).

Riesz transform

Laplacian with drift

Littlewood-Paley-Stein function

Real hyperbolic space


H. Q. Li

Fudan University

Peter Sjögren

Chalmers, Mathematical Sciences

University of Gothenburg

Potential Analysis

0926-2601 (ISSN) 1572-929X (eISSN)

Vol. 46 3 463-484

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