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Limit formulas for groups with one conjugacy class of Cartan subgroups

Mladen Božičević (2008)

Annales de l’institut Fourier

Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on the flag variety...

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].)

Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups

Guorong Hu (2019)

Czechoslovak Mathematical Journal

We give a characterization of the Hölder-Zygmund spaces 𝒞 σ ( G ) ( 0 < σ < ∞ ) on a stratified Lie group G in terms of Littlewood-Paley type decompositions, in analogy to the well-known characterization of the Euclidean case. Such decompositions are defined via the spectral measure of a sub-Laplacian on G , in place of the Fourier transform in the classical setting. Our approach mainly relies on almost orthogonality estimates and can be used to study other function spaces such as Besov and Triebel-Lizorkin spaces...

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

Yong Ding, Xinfeng Wu (2009)

Studia Mathematica

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

Lp multipliers and their H1-L1 estimates on the Heisenberg group.

Chin-Cheng Lin (1995)

Revista Matemática Iberoamericana

We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.

Lp-estimates for the wave equation on the Heisenberg group.

Detlef Müller, Elias M. Stein (1999)

Revista Matemática Iberoamericana

Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α &gt; (d - 1) |1/p - 1/2|.

Multiplicateurs de Mikhlin pour une classe particulière de groupes non-unimodulaires

Sami Mustapha (1998)

Annales de l'institut Fourier

On montre, pour une classe particulière de groupes non-unimodulaires G = N ⋌ ℝ , où N est un groupe de Lie stratifié et où l’action de ℝ est définie par les dilatations naturelles de N , et pour les sous-laplaciens invariants à gauche correspondants Δ , que toute fonction m ∈ H 2 + ϵ ( ℝ ) possédant un support compact dans ℝ + définit un opérateur m ( Δ ) borné sur les espaces de Lebesgue L p ( G , d r g ) associés à la mesure de Haar invariante à droite sur G , 1 ≤ p ≤ ∞ .

Multiplier theorem on generalized Heisenberg groups II

Waldemar Hebisch, Jacek Zienkiewicz (1996)

Colloquium Mathematicae

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.

Currently displaying 121 – 140 of 243