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

• Autorzy: R. Macías , C. Segovia , J. L. Torrea
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B15: Multipliers
• 42A45: Multipliers
• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 172
• Numer: 2
• Strony: 149-167

Daty

wydano

2006

Twórcy

autor

R. Macías

• IMAL-FIQ, CONICET-Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Argentina

autor

C. Segovia

• Instituto Argentino de Matemática, (IAM)-CONICET, Saavedra 15, 1083 Buenos Aires, Argentina

autor

J. L. Torrea

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm172-2-3