BMO SPACES FOR LAGUERRE EXPANSIONS

Let {phi(alpha)(n)}(n is an element of N) be the Laguerre functions of Hermite type with index alpha. These are eigenfunctions of the Laguerre differential operator L-alpha = 1/2 (-d(2)/dy(2) + y(2) + 1/y(2) (alpha(2) - 1/4)). We define and study a BMO-type space BMOL alpha, which is identified as the dual space of the Hardy-type space associated with La. We characterize BMOL alpha by Carlesson measures related to appropriate square functions. Finally, we prove the boundedness on this space of the fractional integral operator and the Riesz transform related to L-alpha.