Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup

R. Macías, C. Segovia, and J. L. Torrea. "Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup." Studia Mathematica 172.2 (2006): 149-167. <http://eudml.org/doc/284706>.

@article{R2006,
abstract = {We obtain weighted $L^\{p\}$ boundedness, with weights of the type $y^\{δ\}$, δ > -1, for the maximal operator of the heat semigroup associated to the Laguerre functions, $\{ℒ_\{k\}^\{α\}\}_\{k\}$, when the parameter α is greater than -1. It is proved that when -1 < α < 0, the maximal operator is of strong type (p,p) if p > 1 and 2(1+δ)/(2+α) < p < 2(1+δ)/(-α), and if α ≥ 0 it is of strong type for 1 < p ≤ ∞ and 2(1+δ)/(2+α) < p. The behavior at the end points of the intervals where there is strong type is studied in detail and sharp results about the existence or not of strong, weak or restricted types are given.},
author = {R. Macías, C. Segovia, J. L. Torrea},
journal = {Studia Mathematica},
keywords = {heat and Poisson semigroups; Laguerre functions; maximal operator; -boundedness},
language = {eng},
number = {2},
pages = {149-167},
title = {Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup},
url = {http://eudml.org/doc/284706},
volume = {172},
year = {2006},
}

TY - JOUR
AU - R. Macías
AU - C. Segovia
AU - J. L. Torrea
TI - Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup
JO - Studia Mathematica
PY - 2006
VL - 172
IS - 2
SP - 149
EP - 167
AB - We obtain weighted $L^{p}$ boundedness, with weights of the type $y^{δ}$, δ > -1, for the maximal operator of the heat semigroup associated to the Laguerre functions, ${ℒ_{k}^{α}}_{k}$, when the parameter α is greater than -1. It is proved that when -1 < α < 0, the maximal operator is of strong type (p,p) if p > 1 and 2(1+δ)/(2+α) < p < 2(1+δ)/(-α), and if α ≥ 0 it is of strong type for 1 < p ≤ ∞ and 2(1+δ)/(2+α) < p. The behavior at the end points of the intervals where there is strong type is studied in detail and sharp results about the existence or not of strong, weak or restricted types are given.
LA - eng
KW - heat and Poisson semigroups; Laguerre functions; maximal operator; -boundedness
UR - http://eudml.org/doc/284706
ER -