In this paper we study L p -boundedness properties for area LittlewoodPaley functions associated with heat semigroups for Hermite and Laguerre operators.

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In this paper, we study a version of the n-dimensional Hankel transform on certain spaces ℋ μ which were studied in [Molina, S., 2003, A generalization of the spaces ℋ μ and and the space of multipliers. Actas del VII Congreso Dr. Antonio Monteiro, pp. 49-56.]. Moreover, we introduce an n-dimensional generalization of Bessel operator and we have studied its properties in relation to the Hankel transform. Moreover, we study some application to the study of the fractional powers of Bessel operator on .