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1
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Estimates for the Poisson kernels and a Fatou type theorem applications to analysis on Siegel domains

100%
Hulanicki A.
Banach Center Publications
|
1995
|
tom 34
|
nr 1
65-77
EN
This is a short description of some results obtained by Ewa Damek, Andrzej Hulanicki, Richard Penney and Jacek Zienkiewicz. They belong to harmonic analysis on a class of solvable Lie groups called NA. We apply our results to analysis on classical Siegel domains.
2
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Asymptotic behavior of the invariant measure for a diffusion related to an NA group

64%
Damek E., Hulanicki A.
Colloquium Mathematicum
|
2006
|
tom 104
|
nr 2
285-309
EN
On a Lie group NA that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, the heat semigroup $μ_t$ generated by a second order subelliptic left-invariant operator $∑_{j = 0}^{m}Y_j + Y$ is considered. Under natural conditions there is a $μ̌_t$-invariant measure m on N, i.e. $μ̌_t*m = m$. Precise asymptotics of m at infinity is given for a large class of operators with Y₀,...,Yₘ generating the Lie algebra of S.
3
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Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group

64%
Damek E., Hulanicki A.
Studia Mathematica
|
1991-1992
|
tom 101
|
nr 1
33-68
EN
On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).
4
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Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains

64%
Damek E., Hulanicki A.
Studia Mathematica
|
2000
|
tom 139
|
nr 2
101-140
EN
Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone
5
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Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups

64%
Damek E., Hulanicki A.
Colloquium Mathematicum
|
1995
|
tom 68
|
nr 1
121-140
6
Content available remote

Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

52%
Cowling M., Giulini S., Hulanicki A., Mauceri G.
Studia Mathematica
|
1994
|
tom 111
|
nr 2
103-121
EN
We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for $L^1(AN),$ but also for $L^p(AN)$, where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.
7
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Estimates for the Poisson kernels and their derivatives on rank one NA groups

52%
Damek E., Hulanicki A., Zienkiewicz J.
Studia Mathematica
|
1997
|
tom 126
|
nr 2
115-148
EN
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
8
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Pluriharmonic functions on symmetric tube domains with BMO boundary values

52%
Damek E., Dziubański J., Hulanicki A., Torrea J.
Colloquium Mathematicum
|
2002
|
tom 94
|
nr 1
67-86
EN
Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.
9
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A nilpotent Lie algebra and eigenvalue estimates

52%
Dziubański J., Hulanicki A., Jenkins J.
Colloquium Mathematicum
|
1995
|
tom 68
|
nr 1
7-16
EN
The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on $ℝ^n$ with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.
10
Content available remote

On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups

51%
Dziubański J., Hulanicki A.
Studia Mathematica
|
1989
|
tom 94
|
nr 1
81-95
11
Content available remote

Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators

51%
Hulanicki A., Jenkins J. W.
Studia Mathematica
|
1984
|
tom 80
|
nr 3
235-244
12
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

A semi-group of probability measures with non-smooth differentiable densities on a Lie group

51%
Głowacki P., Hulanicki A.
Colloquium Mathematicum
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1987
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tom 51
|
nr 1
131-139
13
Content available remote

Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II

51%
Hulanicki A., Jenkins J. W.
Studia Mathematica
|
1987
|
tom 87
|
nr 3
239-252
14
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Growth of the norms of products of randomly dilated functions from A(T)

45%
Garyga H., Hulanicki A.
Colloquium Mathematicum
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1988
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tom 55
|
nr 2
317-322
15
Content available remote

A functional calculus for Rockland operators on nilpotent Lie groups

44%
Hulanicki A.
Studia Mathematica
|
1984
|
tom 78
|
nr 3
253-266
16
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Exchange of independent sets in abstract algebras I

39%
Hulanicki A., Marczewski E., Mycielski J.
Colloquium Mathematicum
|
1966
|
tom 14
|
nr 1
203-215
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