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On Mackey topology for groups

M. Chasco, E. Martín-Peinador, V. Tarieladze (1999)

Studia Mathematica

The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework...

On Maximal Function on the Laguerre Hypergroup

Guliyev, Vagif, Assal, Miloud (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35Let K = [0, ∞)×R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we consider the generalized shift operator, generated by Laguerre hypergroup, by means of which the maximal function is investigated. For 1 < p ≤ ∞ the Lp(K)-boundedness and weak L1(K)-boundedness result for the maximal function is obtained.* V. Guliyev partially supported by grant of INTAS...

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 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...

Currently displaying 101 – 120 of 259