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

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Macías R., Segovia C., Torrea J.

Studia Mathematica

2006

tom 172

nr 2

149-167

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.

Ograniczanie wyników

1 Studia Mathematica

1 Macías R.

1 Segovia C.

1 Torrea J.

1 2006

Wyniki wyszukiwania

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