Summability on non-rectifiable Jordan curves

Summability on non-rectifiable Jordan curves AbstractFor a given parameterization of a Jordan curve, we define the notion of summability or classes of measurable functions on a contour where a new integral is introduced.It is shown that natural functional spaces defining summability for non-rectifiable Jordan curves are the Lebesgue spaces with the weighted norm.For non-rectifiable Jordan curves where an integral was previously defined for continuous (Hölder) functions [Y. Guseynov,Integrable boundaries and fractals for Hölder classes; the Gauss–Green theorem,Calc. Var. Partial Differential Equations 55 2016, 4, Article ID 103], a weight function is constructed which, in general, is not summable by parameter, and a weighted functional space (summability) is defined where the new integral exists. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Summability on non-rectifiable Jordan curves

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Publisher
De Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
D.O.I.
10.1515/gmj-2018-0031
Publisher site
See Article on Publisher Site

Abstract

AbstractFor a given parameterization of a Jordan curve, we define the notion of summability or classes of measurable functions on a contour where a new integral is introduced.It is shown that natural functional spaces defining summability for non-rectifiable Jordan curves are the Lebesgue spaces with the weighted norm.For non-rectifiable Jordan curves where an integral was previously defined for continuous (Hölder) functions [Y. Guseynov,Integrable boundaries and fractals for Hölder classes; the Gauss–Green theorem,Calc. Var. Partial Differential Equations 55 2016, 4, Article ID 103], a weight function is constructed which, in general, is not summable by parameter, and a weighted functional space (summability) is defined where the new integral exists.

Journal

Georgian Mathematical Journalde Gruyter

Published: Jun 1, 2018

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