Let
,
, and
let
be
a self-adjoint extension of the differential operator
on
as the natural domain. We investigate the weighted estimates of singular
integrals in the Laguerre setting including the maximal function, the Riesz
transform and the square functions associated to the Laguerre operator
. In the special
case of the Riesz transform, we complete the description of the Riesz transform for the full
range of
which significantly improves a result of Nowak and Stempak (J. Funct. Anal.244:2 (2007),
399–443) for
for
.
Keywords
Laguerre function expansion, heat kernel, Riesz transform,
square function, maximal function