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Scaled-oscillation and regularity |
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| Authors: | Zoltá n M Balogh Marianna Csö rnyei |
| Institution: | Mathematisches Institut, Universität Bern, CH--3012 Sidlerstrasse 5, Bern, Switzerland ; Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom |
| 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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