Weak-type Inequalities for higher order Riesz-Laguerre Transforms

摘要

In this paper we study the weak-type (1,1) boundedness of the\udhigher order Riesz-Laguerre transforms associated with the Laguerre\udpolynomials. In particular, we obtain the boundedness for the\udRiesz-Laguerre transforms of order 2 and we find also the sharp\udpolynomial weight w that makes the Riesz-Laguerre transforms\udof order greater than two continuous from L^1(d w mu_alpha)\udinto L^{infty}(d mu_alpha), being mu_alpha the Laguerre measure.