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1
Content available remote

On operators satisfying the Rockland condition

100%
Hebisch W.
Studia Mathematica
|
1998
|
tom 131
|
nr 1
63-71
EN
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.
2
Content available remote

Multiplier theorem on generalized Heisenberg groups

100%
Hebisch W.
Colloquium Mathematicum
|
1993
|
tom 65
|
nr 2
231-239
3
Content available remote

Boundedness of $L^1$ spectral multipliers for an exponential solvable Lie group

100%
Hebisch W.
Colloquium Mathematicum
|
1997
|
tom 73
|
nr 1
155-164
4
Content available remote

Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups

75%
Hebisch W.
Studia Mathematica
|
1989-1990
|
tom 95
|
nr 1
93-106
5
Content available remote

Pointwise estimates for densities of stable semigroups of measures

64%
Głowacki P., Hebisch W.
Studia Mathematica
|
1993
|
tom 104
|
nr 3
243-258
EN
Let ${μ_t}$ be a symmetric α-stable semigroup of probability measures on a homogeneous group N, where 0 < α < 2. Assume that $μ_t$ are absolutely continuous with respect to Haar measure and denote by $h_t$ the corresponding densities. We show that the estimate $h_t(x) ≤ tΩ(x/|x|)|x|^{-n-α}$, x≠0, holds true with some integrable function Ω on the unit sphere Σ if and only if the density of the Lévy measure of the semigroup belongs locally to the Zygmund class LlogL(N╲{e}). The problem turns out to be related to the properties of the maximal function $ℳ f(x) = sup_{t>0} 1/t |ʃ_{0}^{t} h_{t-s} ∗ f ∗ h_s(x)ds|$ which, as is proved here, is of weak type (1,1).
6
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Multiplier theorem on generalized Heisenberg groups II

64%
Hebisch W., Zienkiewicz J.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 1
29-36
EN
We prove that on a product of generalized Heisenberg groups, a Hörmander type multiplier theorem for Rockland operators is true with the critical index n/2 + ϵ, ϵ>0, where n is the euclidean (topological) dimension of the group.
7
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Note on semigroups generated by positive Rockland operators on graded homogeneous groups

51%
Dziubański J., Hebisch W., Zienkiewicz J.
Studia Mathematica
|
1994
|
tom 110
|
nr 2
115-126
EN
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 $|p_1(x)| ≤ Cexp(-cτ(x)^{d/(d-1)})$. Moreover, if G is not stratified, more precise estimates of $p_1$ at infinity are given.
8
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Almost everywhere summability of eigenfunction expansions associated to elliptic operators

50%
Hebisch W.
Studia Mathematica
|
1990
|
tom 96
|
nr 3
263-275
9
Content available remote

A smooth subadditive homogeneous norm on a homogeneous group

38%
Hebisch W., Sikora A.
Studia Mathematica
|
1990
|
tom 96
|
nr 3
231-236
10
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A multiplier theorem for Schrödinger operators

38%
Hebisch W.
Colloquium Mathematicum
|
1990
|
tom 60-61
|
nr 2
659-664
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