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 w that makes the Riesz-Laguerre transforms of order greater than two continuous from L^1(d w mu_alpha) into L^{infty}(d mu_alpha), being mu_alpha the Laguerre measure.
Weak-type Inequalities for higher order Riesz-Laguerre Transforms
SASSO, EMANUELA;
2009-01-01
Abstract
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 w that makes the Riesz-Laguerre transforms of order greater than two continuous from L^1(d w mu_alpha) into L^{infty}(d mu_alpha), being mu_alpha the Laguerre measure.
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