Let G be the Lie group R^2 x R^+ endowed with the Riemannian symmetric space structure. Let X_0, X_1, X_2 be a distinguished basis of left-invariant vectori fields of the L:ie algebra of G and L be the associated Laplacian. We consider the Riesz transform of the firts order associated with L and their adjoint operators and investigate their boundedness properties on a suitable Hardy space H^1. We also study the boundedness of the second order Riesz transforms associated with L.

Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth / Sjogren, P; Vallarino, Maria. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 0373-0956. - STAMPA. - 58:(2008), pp. 1117-1151.

Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth

VALLARINO, MARIA
2008

Abstract

Let G be the Lie group R^2 x R^+ endowed with the Riemannian symmetric space structure. Let X_0, X_1, X_2 be a distinguished basis of left-invariant vectori fields of the L:ie algebra of G and L be the associated Laplacian. We consider the Riesz transform of the firts order associated with L and their adjoint operators and investigate their boundedness properties on a suitable Hardy space H^1. We also study the boundedness of the second order Riesz transforms associated with L.
2008
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2386656