Verification of the sharp inequalities for higher order riesz-laguerre transforms

Abstract EN

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 fromL1 (wduα) into L1,∞(duα),under specific value α ,where μα is the Laguerre measure.