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On the essential unboundedness in measure of sequences of superlinear operators in classes L φ(L)
Stockholm University, Faculty of Science, Department of Mathematics. KHT Royal Institute of Technology, Sweden.
Number of Authors: 12016 (English)In: Transactions of A. Razmadze Mathematical Institute, ISSN 2346-8092, Vol. 170, no 1, p. 19-33Article in journal (Refereed) Published
Abstract [en]

We establish a general theorem for a wide class of sequences of superlinear operators {T-n : L-1(I-2) -> L-0(I-2), n = 1, 2,...} about existence of a function g from a certain class L phi(L) such that the sequence of functions {T-n(g), n = 1, 2,...} is essentially unbounded in measure on I-2. This theorem implies several results about divergence of sequences of classical operators. (C) 2016 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.

Place, publisher, year, edition, pages
2016. Vol. 170, no 1, p. 19-33
Keywords [en]
Essential divergence in measure, Orthogonal Fourier series, Lebesgue functions, Superlinear operators
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-175559DOI: 10.1016/j.trmi.2016.01.001ISI: 000405166800003OAI: oai:DiVA.org:su-175559DiVA, id: diva2:1367723
Available from: 2019-11-05 Created: 2019-11-05 Last updated: 2019-11-05Bibliographically approved

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