Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Jacek Dziubański; Waldemar Hebisch; Jacek Zienkiewicz

Displaying similar documents to “Note on semigroups generated by positive Rockland operators on graded homogeneous groups”

Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II

Andrzej Hulanicki, Joe Jenkins (1987)

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Malliavin calculus for stable processes on homogeneous groups

Piotr Graczyk (1991)

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Let ${μ_{t}}_{t > 0}$ be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures $μ_{t}$ have smooth densities.

Function spaces of Nikolskii type on compact manifold

Cristiana Bondioli (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Nikolskii spaces were defined by way of translations on $R^{n}$ and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in $R^{n}$ , we get an equivalent definition if we replace translations by all isometries of $R^{n}$ . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for...

Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group

Ewa Damek (1992)

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Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group

Ewa Damek, Andrzej Hulanicki (1991)

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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).

Weighted two-parameter Bergman space inequalities.

J. Michael Wilson (2003)

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On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

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C. Watari [12] obtained a simple characterization of Lipschitz classes $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ on the dyadic group using the $L^{p}$ -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p, q}^{α}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p, q}^{α}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...

Limit semigroups of Stancu-Mühlbach operators associated with positive projections

Michele Campiti (1992)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Nonconvolution transforms with oscillating kernels that map $Ḃ_{1}^{0, 1}$ into itself

G. Sampson (1993)

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We consider operators of the form $(Ω f) (y) = ʃ_{- \infty}^{\infty} Ω (y, u) f (u) d u$ with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and $h \in L^{\infty}$ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space $Ḃ_{1}^{0, 1}$ (= B) into itself. In particular, all operators with $h (y) = e^{{i | y |}^{a}}$ , a > 0, a ≠ 1, map B into itself.