## Real Analysis Exchange

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

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

#### 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