For a Lie group G with left-invariant Haar measure and associated Lebesgue spaces L^p(G), we consider the heat kernels {p_t\}_{t>0} arising from a right-invariant Laplacian Δ on G: that is, u(t, .) = p_t * f solves the heat equation (∂/∂t - Δ)u = 0 with initial condition u(0, .) = f(.). We establish weak-type (1, 1) estimates for the maximal operator M (M f = \sup_{t>0} |p_t * f|) and for related Hardy-Littlewood maximal operators in a variety of contexts, namely for groups of polynomial growth and for a number of classes of Iwasawa AN groups. We also study the "local" maximal operator M_0 (M_0 f = \sup_{0<t<1} |p_t * f|) and related Hardy-Littlewood operators for all Lie groups.

Weak type (1,1) estimates for heat kernel maximal functions on Lie groups

GIULINI, SAVERIO;MAUCERI, GIANCARLO
1991-01-01

Abstract

For a Lie group G with left-invariant Haar measure and associated Lebesgue spaces L^p(G), we consider the heat kernels {p_t\}_{t>0} arising from a right-invariant Laplacian Δ on G: that is, u(t, .) = p_t * f solves the heat equation (∂/∂t - Δ)u = 0 with initial condition u(0, .) = f(.). We establish weak-type (1, 1) estimates for the maximal operator M (M f = \sup_{t>0} |p_t * f|) and for related Hardy-Littlewood maximal operators in a variety of contexts, namely for groups of polynomial growth and for a number of classes of Iwasawa AN groups. We also study the "local" maximal operator M_0 (M_0 f = \sup_{0
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/246169
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