{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:50:47Z","timestamp":1765547447816,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"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>We develop novel extensions in the theory of weighted Lorentz spaces. In particular, we generalize classical results by introducing variable-exponent Lorentz spaces, establish sharp constants and quantitative bounds for maximal operators, and extend the framework to encompass fractional maximal operators. Moreover, we analyze endpoint cases through the study of oscillation operators and reveal new connections with weighted Hardy spaces. These results provide a unifying approach that not only refines existing inequalities but also opens new avenues in harmonic analysis and partial differential equations.<\/jats:p>","DOI":"10.3390\/axioms14080562","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T07:54:26Z","timestamp":1753343666000},"page":"562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Weighted Lorentz Spaces, Variable Exponent Analysis, and Operator Extensions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1167-5006","authenticated-orcid":false,"given":"Saeed","family":"Hashemi Sababe","sequence":"first","affiliation":[{"name":"Campus Saint-Jean, University of Alberta, 8406 91 Street, Edmonton, AB T6C 4G9, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7989-1613","authenticated-orcid":false,"given":"Ismail","family":"Nikoufar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Payame Noor University, Tehran 19395-4697, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1090\/S0002-9947-1972-0293384-6","article-title":"Weighted norm inequalities for the Hardy maximal function","volume":"165","author":"Muckenhoupt","year":"1972","journal-title":"Trans. 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Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press.","DOI":"10.1515\/9781400883929"},{"key":"ref_10","unstructured":"Garcia-Cuerva, J., and Rubio de Francia, J.L. (1985). Weighted Norm Inequalities and Related Topics, Elsevier. North-Holland Mathematics Studies."},{"key":"ref_11","unstructured":"Agora, E., Antezana, J., Baena-Miret, S., and Carro, M.J. (2024). Revisiting Yano and Zygmund Extrapolation Theory. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Diening, L., Harjulehto, P., H\u00e4st\u00f6, P., and Ruzicka, M. (2011). Lebesgue and Sobolev Spaces with Variable Exponents, Springer.","DOI":"10.1007\/978-3-642-18363-8"},{"key":"ref_13","unstructured":"Bennett, C., and Sharpley, R. (1988). Interpolation of Operators, Academic Press."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bergh, J., and L\u00f6fstr\u00f6m, J. (1976). Interpolation Spaces. An Introduction, Springer.","DOI":"10.1007\/978-3-642-66451-9"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/562\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:15:02Z","timestamp":1760033702000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,24]]},"references-count":14,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["axioms14080562"],"URL":"https:\/\/doi.org\/10.3390\/axioms14080562","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,7,24]]}}}