Real Analysis Exchange

On the Mixed Derivatives of a Separately Twice Differentiable Function

Volodymyr Mykhaylyuk

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Abstract

We prove that a function $f(x,y)$ of real variables defined on a rectangle, having partial derivatives $f''_{xx}, f''_{yy}\in L_2([0,1]^2)$, has almost everywhere mixed derivatives $f''_{xy}$ and $f''_{yx}$.

Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 293-306.

Dates
First available in Project Euclid: 30 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490839332

Mathematical Reviews number (MathSciNet)
MR3597321

Zentralblatt MATH identifier
06848930

Subjects
Primary: 26B30: Absolutely continuous functions, functions of bounded variation
Secondary: 01A75: Collected or selected works; reprintings or translations of classics [See also 00B60]

Keywords
mixed derivative differentiability integrability measurability Fourier series

Citation

Mykhaylyuk, Volodymyr. On the Mixed Derivatives of a Separately Twice Differentiable Function. Real Anal. Exchange 41 (2016), no. 2, 293--306. https://projecteuclid.org/euclid.rae/1490839332


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