In this paper we study generalized Besov type spaces on the Laguerre hypergroup and we give some characterizations using different equivalent norms which allows to reach results of completeness, continuous embeddings and density of some subspaces. A generalized Calderón-Zygmund formula adapted to the harmonic analysis on the Laguerre Hypergroup is obtained inducing two more equivalent norms.
2000 Mathematics Subject Classification: 42B20, 42B25, 42B35 Let 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...
2000 Mathematics Subject Classification: 35E45 In this paper we study generalized Sobolev spaces H^sG of exponential type associated with the Dunkl operators based on the space G of test functions for generalized hyperfunctions and investigate their properties. Moreover, we introduce a class of symbols of exponential type and their associated pseudodifferential operators related to the Dunkl operators, which act naturally on H^sG.
Mathematics Subject Classification: 42B35, 35L35, 35K35 In this paper we study generalized Strichartz inequalities for the wave equation on the Laguerre hypergroup using generalized homogeneous Besov-Laguerre type spaces.
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