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Displaying 181 – 200 of 323

On convergence for the square root of the Poisson kernel in symmetric spaces of rank 1

Jan-Olav Rönning (1997)

Studia Mathematica

Let P(z,β) be the Poisson kernel in the unit disk , and let $P_{λ} f (z) = ʃ_{\partial} P {(z, φ)}^{1 / 2 + λ} f (φ) d φ$ be the λ -Poisson integral of f, where $f \in L^{p} (\partial)$ . We let $P_{λ} f$ be the normalization $P_{λ} f / P_{λ} 1$ . If λ >0, we know that the best (regular) regions where $P_{λ} f$ converges to f for a.a. points on ∂ are of nontangential type. If λ =0 the situation is different. In a previous paper, we proved a result concerning the convergence of $P_{0} f$ toward f in an $L^{p}$ weakly tangential region, if $f \in L^{p} (\partial)$ and p > 1. In the present paper we will extend the result to symmetric spaces X of...

On Deny's characterization of the potential kernel for a convolution Feller semi-group

John C. Taylor (1975)

Annales de l'institut Fourier

The convolution kernels $V f = f * x$ on a homogeneous space $E = G / K$ , where $K$ is a compact sub-group of $G$ , that satisfy the complete maximum principle are characterized.Deny’s result for abelian groups $G$ , but with a stronger hypothesis, is a special case.

On Eigenspaces of the Hecke Algebra with Respect to a Good Maximal Compact Subgroup of ap-Adic Reductive Group.

Shin-ichi Kato (1981)

Mathematische Annalen

On fractional differentiation and integration on spaces of homogeneous type.

A. Eduardo Gatto, Carlos Segovia, Stephen Vági (1996)

Revista Matemática Iberoamericana

In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before.We show that these operators act on Lipschitz spaces as in the classical cases. We prove that...

On limit multiplicities of discrete series representations in spaces of automorphic forms.

Laurent Clozel (1986)

Inventiones mathematicae

On maximal functions over circular sectors with rotation invariant measures

Hugo A. Aimar, Liliana Forzani, Virginia Naibo (2001)

Commentationes Mathematicae Universitatis Carolinae

Given a rotation invariant measure in $ℝ^{n}$ , we define the maximal operator over circular sectors. We prove that it is of strong type $(p, p)$ for $p > 1$ and we give necessary and sufficient conditions on the measure for the weak type $(1, 1)$ inequality. Actually we work in a more general setting containing the above and other situations.

On mean periodic functions on complex hyperbolic spaces.

Volchkov, Vit.V. (2002)

Sibirskij Matematicheskij Zhurnal

On molecules and fractional integrals on spaces of homogeneous type with finite measure

A. Gatto, Stephen Vági (1992)

Studia Mathematica

In this paper we prove the continuity of fractional integrals acting on nonhomogeneous function spaces defined on spaces of homogeneous type with finite measure. A definition of the molecules which are used in the $H^{p}$ theory is given. Results are proved for $L^{p}$ , $H^{p}$ , BMO, and Lipschitz spaces.

On positive Rockland operators

Pascal Auscher, A. ter Elst, Derek Robinson (1994)

Colloquium Mathematicae

Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on $L_{p} (G; d g)$ . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on $L_{2}$ we prove that it is closed on each of the $L_{p}$ -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the $L_{p}$ -spaces, p ∈ [1,∞]. Further extensions...

On some causal and conformal groups.

Bertram, Wolfgang (1996)

Journal of Lie Theory

On some dimension problems for self-affine fractals.

Bernardi, M.P., Bondioli, C. (1999)

Zeitschrift für Analysis und ihre Anwendungen

On some series of representations related to symmetric spaces

H. Schlichtkrull (1984)

Mémoires de la Société Mathématique de France

On s-sets and mutual absolute continuity of measures on homogeneous spaces.

Tord Sjödin (1997)

Manuscripta mathematica

On the causal structure of Lorentzian Lie groups. A globality theorem for Lorentzian cones in certain solvable Lie algebras.

Dirk Mittenhuber (1996)

Mathematische Annalen

On the Convergence and Divergence Behaviour of Approximation Processes in Homogeneous Banach Spaces.

Walter Schempp, Bernd Dreseler (1975)

Mathematische Zeitschrift

On the Corwin-Greenleaf conjecture. (Sur la conjecture de Corwin-Greenleaf.)

Fujiwara, Hidenori (1997)