𝐿_{𝑝} derivatives and approximate Peano derivatives

Evans, Michael J.

doi:10.1090/S0002-9947-1972-0293030-1

$L _{p}$ derivatives and approximate Peano derivatives
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by Michael J. Evans PDF

Trans. Amer. Math. Soc. 165 (1972), 381-388 Request permission

Abstract:

It is known that approximate derivatives and kth Peano derivatives share several interesting properties with ordinary derivatives. In this paper the author points out that kth ${L_p}$ derivatives also share these properties. Furthermore, a definition for a kth approximate Peano derivative is given which generalizes the notions of a kth Peano derivative, a kth ${L_p}$ derivative, and an approximate derivative. It is then shown that a kth approximate Peano derivative at least shares the property of belonging to Baire class one with these other derivatives.

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