Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

Let ℍn be the Heisenberg group. The fundamental manifold of the radial function space for ℍn can be denoted by [0,+∞)×ℝ, which is just the Laguerre hypergroup. In this paper the multiresolution analysis on the Laguerre hypergroup 𝕂=[0,+∞)×ℝ is defined. Moreover the properties of Haar wavelet bases for La2(𝕂) are investigated

On Maximal Function on the Laguerre Hypergroup

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 (Project 05-1000008-8157)

Generalized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup

Mathematics Subject Classification: 42B35, 35L35, 35K35In this paper we study generalized Strichartz inequalities for the wave equation on the Laguerre hypergroup using generalized homogeneous Besov-Laguerre type spaces

Bessel potential space on the Laguerre hypergroup

<p>Abstract</p> <p>In this article, we define the fractional differentiation <it>D_&#948;</it>of order <it>&#948;</it>, <it>&#948; </it>> 0, induced by the Laguerre operator <it>L </it>and associated with respect to the Haar measure d<it>m_&#945;</it>. We obtain a characterization of the Bessel potential space <inline-formula><graphic file="1687-1847-2011-4-i1.gif"/></inline-formula> using <it>D_&#948;</it>and different equivalent norms.</p