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1
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Composition and L²-boundedness of flag kernels

100%
Głowacki P.
Colloquium Mathematicum
|
2010
|
tom 118
|
nr 2
581-585
EN
We prove the composition and L²-boundedness theorems for the Nagel-Ricci-Stein flag kernels related to the natural gradation of homogeneous groups.
2
Content available remote

The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

100%
Głowacki P.
Studia Mathematica
|
1998
|
tom 127
|
nr 2
169-190
EN
Let A be a pseudodifferential operator on $ℝ^N$ whose Weyl symbol a is a strictly positive smooth function on $W = ℝ^N × ℝ^N$ such that $|∂^{α}a| ≤ C_αa^{1-ϱ}$ for some ϱ>0 and all |α|>0, $∂^{α}a$ is bounded for large |α|, and $lim_{w→∞}a(w) = ∞$. Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin.
3
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Correction to "Composition and L²-boundedness of flag kernels" (Colloq. Math. 118 (2010), 581-585)

100%
Głowacki P.
Colloquium Mathematicum
|
2010
|
tom 120
|
nr 2
4
Content available remote

Lipschitz continuity of densities of stable semigroups of measures

100%
Głowacki P.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 1
29-47
EN
In this paper we raise the question of regularity of the densities $h_t$ of a symmetric stable semigroup ${μ_t}$ of measures on the homogeneous group N under the mere assumption that the densities exist. (For a criterion of the existence of the densities of such semigroups see [11].)
5
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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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A semi-group of probability measures with non-smooth differentiable densities on a Lie group

51%
Głowacki P., Hulanicki A.
Colloquium Mathematicum
|
1987
|
tom 51
|
nr 1
131-139
7
Content available remote

An inversion problem for singular integral operators on homogeneous groups

44%
Głowacki P.
Studia Mathematica
|
1987
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tom 87
|
nr 1
53-69
8
Content available remote

A calculus of symbols and convolution semigroups on the Heisenberg group

38%
Głowacki P.
Studia Mathematica
|
1982
|
tom 72
|
nr 3
291-321
9
Content available remote

The Rockland condition for nondifferential convolution operators II

38%
Głowacki P.
Studia Mathematica
|
1991
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tom 98
|
nr 2
99-114
10
Content available remote

Stable semi-groups of measures on the Heisenberg group

32%
Głowacki P.
Studia Mathematica
|
1984
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tom 79
|
nr 2
105-138
11
Content available remote

On functions with scattered spectra on lea groups

26%
Głowacki P.
Studia Mathematica
|
1981
|
tom 70
|
nr 2
147-152
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