In this paper, we provide a Taylor formula with integral remainder in the setting of homogeneous groups in the sense of Folland and Stein. This formula allows us to give a simplified proof of the so-called `Taylor inequality'. As a by-product, we furnish an explicit expression for the relevant Taylor polynomials. Applications are provided. Among others, it is given a sufficient condition for the real-analiticity of a function whose higher order derivatives (in the sense of the Lie algebra) satisfy a suitable growth condition. Moreover, we prove the `L-harmonicity' of the Taylor polynomials related to a `L-harmonic' function, when L is a general homogenous left-invariant differential operator on a homogeneous group. (This result is one of the ingredients for obtaining Schauder estimates related to L).

A. Bonfiglioli (2008). Taylor formula for homogeneous groups and applications (Italian Title: La Formula di Taylor per i Gruppi Omogenei ed Applicazioni). SEMINARI DI ANALISI MATEMATICA BRUNO PINI, Anno Accademico 2007/2008, 43-69.

Taylor formula for homogeneous groups and applications (Italian Title: La Formula di Taylor per i Gruppi Omogenei ed Applicazioni)

BONFIGLIOLI, ANDREA
2008

Abstract

In this paper, we provide a Taylor formula with integral remainder in the setting of homogeneous groups in the sense of Folland and Stein. This formula allows us to give a simplified proof of the so-called `Taylor inequality'. As a by-product, we furnish an explicit expression for the relevant Taylor polynomials. Applications are provided. Among others, it is given a sufficient condition for the real-analiticity of a function whose higher order derivatives (in the sense of the Lie algebra) satisfy a suitable growth condition. Moreover, we prove the `L-harmonicity' of the Taylor polynomials related to a `L-harmonic' function, when L is a general homogenous left-invariant differential operator on a homogeneous group. (This result is one of the ingredients for obtaining Schauder estimates related to L).
2008
A. Bonfiglioli (2008). Taylor formula for homogeneous groups and applications (Italian Title: La Formula di Taylor per i Gruppi Omogenei ed Applicazioni). SEMINARI DI ANALISI MATEMATICA BRUNO PINI, Anno Accademico 2007/2008, 43-69.
A. Bonfiglioli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/128949
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