Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 491-507
Chalmers and University of Gothenburg, Department of Mathematical Sciences
S-412 96 Göteborg, Sweden; peters 'at' chalmers.se
Politecnico di Torino, Dipartimento di Scienze Matematiche
Corso Duca degli Abruzzi, 24, 10129 Torino, Italy; maria.vallarino 'at' polito.it
Abstract. Let G be the Lie group R2 \rtimes R+ 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 define the Laplacian \Delta = -(X02 + X12 + X22). In this paper, we show that the maximal function associated with the heat kernel of the Laplacian \Delta 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.
2010 Mathematics Subject Classification: Primary 22E30, 35K08, 42B25, 42B30.
Key words: Heat kernel, maximal function, Hardy space, Lie groups, exponential growth.
Reference to this article: P. Sjögren and M. Vallarino: Heat maximal function on a Lie group of exponential growth. Ann. Acad. Sci. Fenn. Math. 37 (2012), 491-507.
doi:10.5186/aasfm.2012.3729
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