Let G be the Lie group R^2xR^+ endowed with the Riemannian symmetric space structure. Let X_0, X_1, X_2 be a distinguished basis of left invariant vector fields of the Lie algebra of G and define the Laplacian L=-(X_0^2+X_1^2+X_2^2). In this paper, we show that the maximal function associated with the heat kernel of the Laplacian L is bounded from the Hardy space H^1 to L^1. We also prove that the heat maximal function does not provide a maximal characterization of the Hardy space H^1.

Heat maximal function on a Lie group of exponential growth / Sjogren, P.; Vallarino, Maria. - In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA. - ISSN 1239-629X. - STAMPA. - 37:(2012), pp. 491-507.

Heat maximal function on a Lie group of exponential growth

VALLARINO, MARIA
2012

Abstract

Let G be the Lie group R^2xR^+ endowed with the Riemannian symmetric space structure. Let X_0, X_1, X_2 be a distinguished basis of left invariant vector fields of the Lie algebra of G and define the Laplacian L=-(X_0^2+X_1^2+X_2^2). In this paper, we show that the maximal function associated with the heat kernel of the Laplacian L is bounded from the Hardy space H^1 to L^1. We also prove that the heat maximal function does not provide a maximal characterization of the Hardy space H^1.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2498438