Finite first and second symmetric Borel derivatives of f imply symmetric distributional point values for T_f' and T_f'' respectively, with one-sided and smoothness conditions also addressed.
Mukhopadhyay,Higher Order Derivatives, Chapman and Hall/CRC, Boca Raton, 2012
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Distributional Point Values for Borel and Symmetric Borel Derivatives
Finite first and second symmetric Borel derivatives of f imply symmetric distributional point values for T_f' and T_f'' respectively, with one-sided and smoothness conditions also addressed.