{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:44:49Z","timestamp":1760143489035,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:00:00Z","timestamp":1706659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Some fundamental properties of the Muckenhoupt class Ap of weights and the Gehring class Gq of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based on proving some properties of integral operators on time scales with powers and certain mathematical relations connecting the norms of Muckenhoupt and Gehring classes. The results as special cases cover the results for functions following David Cruz-Uribe, C. J. Neugebauer, and A. Popoli, and when the time scale equals the positive integers, the results for sequences are essentially new.<\/jats:p>","DOI":"10.3390\/axioms13020098","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T10:44:24Z","timestamp":1706697864000},"page":"98","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-2370","authenticated-orcid":false,"given":"Ravi P.","family":"Agarwal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4245-4364","authenticated-orcid":false,"given":"Mohamed Abdalla","family":"Darwish","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Damanhour University, Damanhour 22514, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamdi Ali","family":"Elshamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Damanhour University, Damanhour 22514, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2793-0972","authenticated-orcid":false,"given":"Samir H.","family":"Saker","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Mansoura University, Mansoura 35516, Egypt"},{"name":"Department of Mathematics, Faculty of Science, New Mansoura University, New Mansoura City 7723730, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/BF03323153","article-title":"Analysis on measure chains-a unified approach to continuous and discrete calculus","volume":"18","author":"Hilger","year":"1990","journal-title":"Results Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bohner, M., and Peterson, A. 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