Real Analysis Exchange

Relation Between $L_{p}$-Derivates and Peano, Approximate Peano and Borel Derivates of Higher Order

S. N. Mukhopadhyay and S. Ray

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The definition of the $L_{p}$-derivative is such that it involves only the absolute value of the function and therefore the definition of $L_{p}$-derivates is not possible from the definition of $L_{p}$-derivative. Therefore, a special technique is used to define them and relations between $L_{p}$-derivates and Peano, approximate Peano and Borel derivates are studied.

Article information

Source
Real Anal. Exchange, Volume 41, Number 1 (2016), 137-158.

Dates
First available in Project Euclid: 29 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490752821

Mathematical Reviews number (MathSciNet)
MR3511940

Zentralblatt MATH identifier
06848920

Subjects
Primary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
Secondary: 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives

Keywords
Upper and lower $L_p$-derivates Peano approximate Peano derivative approximate Borel derivate Minkowski’s inequality Holder’s inequality

Citation

Mukhopadhyay, S. N.; Ray, S. Relation Between $L_{p}$-Derivates and Peano, Approximate Peano and Borel Derivates of Higher Order. Real Anal. Exchange 41 (2016), no. 1, 137--158. https://projecteuclid.org/euclid.rae/1490752821


Export citation