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Stable semi-groups of measures as commutative approximate identities on non-graded homogeneous groups.

Pawel Glowacki — 1986

Inventiones mathematicae

Lipschitz continuity of densities of stable semigroups of measures

Paweł Głowacki — 1993

Colloquium Mathematicae

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].)

The Rockland condition for nondifferential convolution operators II

Paweł Głowacki — 1991

Studia Mathematica

The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

Paweł Głowacki — 1998

Studia Mathematica

Let A be a pseudodifferential operator on $ℝ^{N}$ whose Weyl symbol a is a strictly positive smooth function on $W = ℝ^{N} \times ℝ^{N}$ such that $| \partial^{α} a | \leq C_{α} a^{1 - ϱ}$ for some ϱ>0 and all |α|>0, $\partial^{α} a$ is bounded for large |α|, and $l i m_{w \to \infty} a (w) = \infty$ . 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.

Stable semi-groups of measures on the Heisenberg group

Paweł Głowacki — 1984

Studia Mathematica

A calculus of symbols and convolution semigroups on the Heisenberg group

Paweł Głowacki — 1982

Studia Mathematica

On functions with scattered spectra on lea groups

Paweł Głowacki — 1981

Studia Mathematica

An inversion problem for singular integral operators on homogeneous groups

Paweł Głowacki — 1987

Studia Mathematica

Composition and L²-boundedness of flag kernels

Paweł Głowacki — 2010

Colloquium Mathematicae

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

Correction to "Composition and L²-boundedness of flag kernels" (Colloq. Math. 118 (2010), 581-585)

Paweł Głowacki — 2010

Colloquium Mathematicae

Pointwise estimates for densities of stable semigroups of measures

Paweł Głowacki; Waldemar Hebisch — 1993

Studia Mathematica

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 $h_{t} {(x) \leq t Ω (x / | x |) | x |}^{- n - α}$ , 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...