Weak-type inequalities for higher order Riesz–Laguerre transforms

In this paper we study the weak-type (1, 1) boundedness of the higher order Riesz–Laguerre transforms associated with the Laguerre polynomials. In particular, we obtain the boundedness for the Riesz–Laguerre transforms of order 2 and we find also the sharp polynomial weight ω that makes the Riesz–Laguerre transforms of order greater than two continuous from L1(ω dμα) into L1,∞ (dμα), being μα the Laguerre measure. © 2008 Elsevier Inc. All rights reserved.