Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space

• Let v not equal 0 be a vector in R-n. Consider the Laplacian on R-n with drift Lambda(v) = Lambda + 2v.del. and the measure d mu(x) = e(2 < v,x.>)dx, with respect to which Delta(v) is self-adjoint. This measure has exponential growth with respect to the Euclidean distance. We study weak type (1, 1) and other sharp endpoint estimates for the Riesz transforms of any order, and also for the vertical and horizontal Littlewood-Paley-Stein functions associated with the heat and the Poisson semigroups.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Riesz transform

Littlewood-Paley-Stein operators

Heat semigroup

Laplacian with drift

paley-stein functions

weak type 1

1

riesz transforms

riemannian-manifolds

singular-integrals

heat kernel

lie-groups

Mathematics

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