Displaying similar documents to “Singular integrals on the complex affine group”

Singular integral operators with non-smooth kernels on irregular domains.

Xuan Thinh Duong, Alan McIntosh (1999)

Revista Matemática Iberoamericana

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Let χ be a space of homogeneous type. The aims of this paper are as follows. i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition. ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a...

Heat kernels and Riesz transforms on nilpotent Lie groups

A. ter Elst, Derek Robinson, Adam Sikora (1998)

Colloquium Mathematicae

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We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian...

On operators satisfying the Rockland condition

Waldemar Hebisch (1998)

Studia Mathematica

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Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.