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Displaying similar documents to “An inversion problem for singular integral operators on homogeneous groups”

Convolution operators on Hardy spaces

Chin-Cheng Lin (1996)

Studia Mathematica

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We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces H p ( G ) , where G is a homogeneous group.

Composition and L²-boundedness of flag kernels

Paweł Głowacki (2010)

Colloquium Mathematicae

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We prove the composition and L²-boundedness theorems for the Nagel-Ricci-Stein flag kernels related to the natural gradation of homogeneous groups.

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.

Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Jacek Dziubański, Waldemar Hebisch, Jacek Zienkiewicz (1994)

Studia Mathematica

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Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let p t be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that | p 1 ( x ) | ≤ C e x p ( - c τ ( x ) d / ( d - 1 ) ) . Moreover, if G is not stratified, more precise estimates of p 1 at infinity are given.

Littlewood-Paley g-functions with rough kernels on homogeneous groups

Yong Ding, Xinfeng Wu (2009)

Studia Mathematica

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Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾

Malliavin calculus for stable processes on homogeneous groups

Piotr Graczyk (1991)

Studia Mathematica

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Let μ t t > 0 be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures μ t have smooth densities.

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...