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Leonid V. Kovalev, Jani Onninen (2009)
Studia Mathematica
We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.
Ponomarev, S.P. (2004)
Sibirskij Matematicheskij Zhurnal
Michel BRUNEAU (1972/1973)
Seminaire de Théorie des Nombres de Bordeaux
Luisa Di Piazza (2001)
Czechoslovak Mathematical Journal
We study properties of variational measures associated with certain conditionally convergent integrals in . In particular we give a full descriptive characterization of these integrals.
Donatella Bongiorno, Luisa Di Piazza, Valentin A. Skvortsov (2006)
Czechoslovak Mathematical Journal
Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a -adic path system that defines a differentiation basis which does not possess Ward property.
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