Abstract:
The weak-type (1, 1) boundedness of the higher order Riesz–Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We show the sharp polynomial weight w that makes the Riesz–Laguerre transforms of order greater than or equal to 2 continuous from? L?^1 (w?d??_? ) into ? L?^(1,?) (?d??_? ) ,under specific value ? ,where ?_? is the Laguerre measure.
