Abstract
The Lusin N-property is well known as a criterion for validity of theorems on change of variables in integral. Here we consider related properties motivated by the coarea formula. They also imply a generalization of Eilenberg’s inequality. We prove them for functions with gradient in the Lorentz space Lm,1. This relies on estimates of Hausdorff content of level sets for Sobolev functions and analysis of their Lebesgue points. A significant part of the presented results has its origin in a joint work with David Swanson and William P. Ziemer.
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1 The research is supported in part by the Research Project MSM 113200007 from the Czech Ministry of Education, Grant No. 201/00/0767 from the Grant Agency of the Czech republic (Ga ČR) and Grant No. 165/99 from the Grant Agency of Charles University(GA UK)
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Malý, J. (2003). Coarea Properties of Sobolev Functions. In: Haroske, D., Runst, T., Schmeisser, HJ. (eds) Function Spaces, Differential Operators and Nonlinear Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8035-0_26
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DOI: https://doi.org/10.1007/978-3-0348-8035-0_26
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