info:eu-repo/semantics/article
A sharp weighted transplantation theorem for Laguerre function expansions
Fecha
2007-03Registro en:
Garrigós, G.; Harboure, Eleonor Ofelia; Signes, T.; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; A sharp weighted transplantation theorem for Laguerre function expansions; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 244; 1; 3-2007; 247-276
0022-1236
CONICET Digital
CONICET
Autor
Garrigós, G.
Harboure, Eleonor Ofelia
Signes, T.
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
Resumen
We find the sharp range of boundedness for transplantation operators associated with Laguerre function expansions in Lp spaces with power weights. Namely, the operators interchanging {Lkα} and {Lkβ} are bounded in Lp (yδ p) if and only if - frac(ρ, 2) - frac(1, p) < δ < 1 - frac(1, p) + frac(ρ, 2), where ρ = min {α, β}. This improves a previous partial result by Stempak and Trebels, which was only sharp for ρ ≤ 0. Our approach is based on new multiplier estimates for Hermite expansions, weighted inequalities for local singular integrals and a careful analysis of Kanjin's original proof of the unweighted case. As a consequence we obtain new results on multipliers, Riesz transforms and g-functions for Laguerre expansions in Lp (yδ p).