Heat maximal function on a Lie group of exponential growth
Journal article, 2012
Let G be the Lie group R2 x R+ (semidirect product) endowed with the Riemannian
symmetric space structure. Let X0; X1; X2 be a distinguished basis of left-invariant
vector fields of the Lie algebra of G and write L for the corresponding Laplacian. In this paper, we show that the maximal function associated
with the heat kernel of L is bounded from the Hardy space H1 to
L1. We also prove that the heat maximal function does not provide a maximal
characterization of the Hardy space H1
Heat kernel
Lie groups
exponential growth
multipliers
rd-spaces
operator
bmo
Hardy space
maximal function
hardy-spaces
h-1
Author
Peter Sjögren
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Maria Vallarino
Annales Academiae Scientiarum Fennicae Mathematica
1239629x (ISSN) 17982383 (eISSN)
Vol. 37 2 491-507Subject Categories (SSIF 2011)
Mathematical Analysis
DOI
10.5186/aasfm.2012.3729