Characterization of relatively compact sets in weighted Lebesgue spaces by weighted modulus of continuity and application

Characterization of relatively compact sets in weighted Lebesgue spaces by weighted modulus of continuity and application | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 10 February 2026 V1 Latest version Share on Characterization of relatively compact sets in weighted Lebesgue spaces by weighted modulus of continuity and application Authors : Aytekin E. Abdullayeva , Rovshan A. Bandaliyev 0000-0002-7613-7113 [email protected] , and Aynur N. Mammadova Authors Info & Affiliations https://doi.org/10.22541/au.177071779.95972349/v1 110 views 50 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper we consider a weighted modulus of continuity in weighted Lebesgue spaces. We proved that the modulus of continuity is well defined in weighted Lebesgue spaces and has all the properties of usual modulus of continuity. Also, we study relatively compact sets in weighted Lebesgue spaces. The full characterization of relatively compact sets is given in the case of weighted Lebesgue space by weighted modulus of continuity. In particular, we give an analog of the Kolmogorov-Riesz compactness theorem in weighted Sobolev spaces by weighted modulus of continuity. As an application, we give an approximation theorem for a family of averaging operators in weighted Lebesgue spaces by a weighted modulus of continuity. Supplementary Material File (new submission.pdf) Download 291.48 KB Information & Authors Information Version history V1 Version 1 10 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords approximation theorem averaging operator compactness theorem weighted lebesgue spaces weighted modulus of continuity weighted sobolev spaces Authors Affiliations Aytekin E. Abdullayeva Ministry of Science and Education of the Republic of Azerbaijan View all articles by this author Rovshan A. Bandaliyev 0000-0002-7613-7113 [email protected] Ministry of Science and Education of the Republic of Azerbaijan View all articles by this author Aynur N. Mammadova Baku Business University View all articles by this author Metrics & Citations Metrics Article Usage 110 views 50 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Aytekin E. Abdullayeva, Rovshan A. Bandaliyev, Aynur N. Mammadova. Characterization of relatively compact sets in weighted Lebesgue spaces by weighted modulus of continuity and application. Authorea . 10 February 2026. DOI: https://doi.org/10.22541/au.177071779.95972349/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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