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In this work we define and study Poisson integral associated with Laplace-Bessel differential operators. We establish weighted inequalities with a general weight for the g Littlewood-Paley functions and the commutator gb,k defined by (1.2) associated with Laplace Bessel differential operator. Mathematics subject classification (2010): Primary 42B20, 42B25, 42B35.

Weighted norm inequalities for the g-Littlewood-Paley operators associated with Laplace-Bessel differential operators