Real Analysis Exchange

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

S. N. Mukhopadhyay and S. Ray

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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

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

First available in Project Euclid: 29 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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