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On certain integral means of functions of generalized bounded variation

On certain integral means of functions of generalized bounded variation AbstractFor certain classes of functions of Λ-bounded variation on [-π,π]{[-\pi,\pi]}, Waterman and D’Antonio constructed a sequence of summability kernels such that the corresponding integral means converge for any function from the class,but not for any function from a broader Λ′⁢BV{\Lambda^{\prime}\mathrm{BV}} class.In our paper, we extend this result to the case of functions of two variables. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On certain integral means of functions of generalized bounded variation

Georgian Mathematical Journal , Volume 28 (2): 7 – Apr 1, 2021

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References (11)

Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2019-2051
Publisher site
See Article on Publisher Site

Abstract

AbstractFor certain classes of functions of Λ-bounded variation on [-π,π]{[-\pi,\pi]}, Waterman and D’Antonio constructed a sequence of summability kernels such that the corresponding integral means converge for any function from the class,but not for any function from a broader Λ′⁢BV{\Lambda^{\prime}\mathrm{BV}} class.In our paper, we extend this result to the case of functions of two variables.

Journal

Georgian Mathematical Journalde Gruyter

Published: Apr 1, 2021

Keywords: Generalized variation; summability kernels; 42B08; 26B30

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