Weak type (1, 1) for some operators related to the Laplacian with drift on real hyperbolic spaces Artikel i vetenskaplig tidskrift, 2017

The setting of this work is the $n$-dimensional hyperbolic space $\R^+ \times \R^{n-1}$, where the Laplacian is given a drift in the $\R^+$ direction. We consider the operators given 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 $L^p,\; 1<p<\infty$, 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). In the exceptional cases, we disprove the weak type (1,1).

Författare

Fudan University

Peter Sjögren

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Potential Analysis

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

46 463 -484

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1007/s11118-016-9590-x

2020-12-16