Local Maximal Function and Operators Associated to Laguerre Expansions

VIOLA, P; VIVIANI, B

TOHOKU MATHEMATICAL JOURNAL

TOHOKU UNIVERSITY

Año: 2014 vol. 66 p. 155 - 169

0040-8735

In this work we consider the heat problem for the Laguerre operator with initial data f belonging to weighted Lebesgue spaces Lp ((0,infty);v dx). We find conditions on a weight v in order to assure a pointwise convergence of its solution, u(x,T), to f when t tends to zero.In proving this we obtain weighted inequalities for the maximal operator in the rango alpha great or equal to 0. In conection with this problem, we get sharp conditions on a weight v we qallow us to obtain some weighted inequalities for a local maximal Hardy-Littlewood operator on an open set in R^n, that we believe are of independent interest. Finally, as a by produc, we obtain weighted inequalities for the Riesz-Laguerre operators.