Scaled-oscillation and regularity

Balogh, Zoltán; Csörnyei, Marianna

doi:10.1090/S0002-9939-06-08290-6

Scaled-oscillation and regularity
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by Zoltán M. Balogh and Marianna Csörnyei PDF

Proc. Amer. Math. Soc. 134 (2006), 2667-2675 Request permission

Abstract:

We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.

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