{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:29:00Z","timestamp":1760146140822,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12061069"],"award-info":[{"award-number":["12061069"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure \u03bc of exponential growth, the authors introduce the variable Lebesgue space Lp(\u00b7)(\u03bc) over (V,d,\u03bc) and investigate it under the global H\u00f6lder continuity condition for p(\u00b7). As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on Lp(\u00b7)(\u03bc) is obtained, and an unbounded example is presented.<\/jats:p>","DOI":"10.3390\/sym16101283","type":"journal-article","created":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T04:57:28Z","timestamp":1727672248000},"page":"1283","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Variable Lebesgue Space over Weighted Homogeneous Tree"],"prefix":"10.3390","volume":"16","author":[{"given":"Yuxun","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1541-5316","authenticated-orcid":false,"given":"Jiang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"200","DOI":"10.4064\/sm-3-1-200-211","article-title":"\u00dcber konjugierte exponentenfolgen","volume":"3","author":"Orlicz","year":"1931","journal-title":"Stud. Math."},{"key":"ref_2","first-page":"592","article-title":"On spaces Lp(x) and Wk,p(x)","volume":"41","year":"1991","journal-title":"Czech. Math. J."},{"key":"ref_3","first-page":"245","article-title":"Maximal function on generalized Lebesgue spaces Lp(\u00b7)","volume":"7","author":"Diening","year":"2004","journal-title":"Math. Inequal. Appl."},{"key":"ref_4","first-page":"255","article-title":"Hardy-Littlewood maximal operator on Lp(x)(Rn)","volume":"7","author":"Nekvinda","year":"2004","journal-title":"Math. Inequal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Cruz-Uribe, D.V., and Fiorenza, A. (2013). Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Springer Science & Business Media.","DOI":"10.1007\/978-3-0348-0548-3"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Coifman, R.R., and Weiss, G. (2006). Analyse Harmonique Non-Commutative sur Certains Espaces Homog\u00e8nes: \u00c9tude de Certaines Int\u00e9grales Singuli\u00e8res, Springer.","DOI":"10.1007\/BFb0058953"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109","DOI":"10.4064\/sm8556-6-2017","article-title":"The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type","volume":"242","author":"Shukla","year":"2018","journal-title":"Stud. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s00209-003-0510-6","article-title":"Multipliers and singular integrals on exponential growth groups","volume":"245","author":"Hebisch","year":"2003","journal-title":"Math. Z."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/978-3-030-36138-9_2","article-title":"Hardy spaces on weighted homogeneous trees","volume":"Volume 1","author":"Arditti","year":"2020","journal-title":"Advances in Microlocal and Time-Frequency Analysis"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8832","DOI":"10.1007\/s12220-020-00435-w","article-title":"BMO spaces on weighted homogeneous trees","volume":"31","author":"Arditti","year":"2021","journal-title":"J. Geom. Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"485","DOI":"10.5565\/PUBLMAT_54210_10","article-title":"A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa","volume":"54","year":"2010","journal-title":"Publ. Mat."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Grafakos, L. (2008). Classical Fourier Analysis, Springer.","DOI":"10.1007\/978-0-387-09432-8"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1283\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:07:26Z","timestamp":1760112446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1283"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,30]]},"references-count":12,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["sym16101283"],"URL":"https:\/\/doi.org\/10.3390\/sym16101283","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,9,30]]}}}