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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 the dual of a Commutative signed Hypergroup.

Margit Rösler (1995)

Manuscripta mathematica

On the Fourier Transformation of Positive, Positive Definite Measure on Commutative Hypergroups, and Dual Convolution Structures.

Michael Voit (1991)

Manuscripta mathematica

On the Hausdorff-Young theorem for commutative hypergroups

Sina Degenfeld-Schonburg (2013)

Colloquium Mathematicae

We study the Hausdorff-Young transform for a commutative hypergroup K and its dual space K̂ by extending the domain of the Fourier transform so as to encompass all functions in $L^{p} (K, m)$ and $L^{p} (K ̂, π)$ respectively, where 1 ≤ p ≤ 2. Our main theorem is that those extended transforms are inverse to each other. In contrast to the group case, this is not obvious, since the dual space K̂ is in general not a hypergroup itself.

Displaying 1 – 4 of 4

On Maximal Function on the Laguerre Hypergroup

On the dual of a Commutative signed Hypergroup.

On the Fourier Transformation of Positive, Positive Definite Measure on Commutative Hypergroups, and Dual Convolution Structures.

On the Hausdorff-Young theorem for commutative hypergroups

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