We consider a Lagrange-Hermite polynomial, interpolating a function at the Jacobi zeros and, with its first (r-1) derivatives, at the points ±1. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator in certain suitable weighted Lp-spaces, 1 < p < 1, proving a Marcinkiewicz inequality involving the derivative of the polynomial at ±1. Moreover, we give optimal estimates for the error of this process also in the weighted uniform metric.
On an interpolation process of Lagrange-Hermite type
Notarangelo I.
2012-01-01
Abstract
We consider a Lagrange-Hermite polynomial, interpolating a function at the Jacobi zeros and, with its first (r-1) derivatives, at the points ±1. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator in certain suitable weighted Lp-spaces, 1 < p < 1, proving a Marcinkiewicz inequality involving the derivative of the polynomial at ±1. Moreover, we give optimal estimates for the error of this process also in the weighted uniform metric.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
MastroianniMilovanovicNotarangeloPIM2012.pdf
Accesso aperto
Dimensione
181.38 kB
Formato
Adobe PDF
|
181.38 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
