{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T02:30:31Z","timestamp":1792809031453,"version":"4.5.0"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T00:00:00Z","timestamp":1722816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2023A1515010614"],"award-info":[{"award-number":["2023A1515010614"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The single generalized weighted composition operator Du,\u03c8n on various spaces of analytic functions has been investigated for decades, i.e., Du,\u03c8nf=u\u00b7(f(n)\u2218\u03c8), where f\u2208H(D). However, the study of the finite sum of generalized weighted composition operators with different orders, i.e., PU,\u03c8kf=u0\u00b7f\u2218\u03c8+u1\u00b7f\u2032\u2218\u03c8+\u22ef+uk\u00b7f(k)\u2218\u03c8, is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of PU,\u03c8k. Specifically, the boundedness and compactness of the sum PU,\u03c8k is equivalent to those of each Dun,\u03c8n, 0\u2264n\u2264k.<\/jats:p>","DOI":"10.3390\/axioms13080530","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T13:57:28Z","timestamp":1722866248000},"page":"530","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sums of Generalized Weighted Composition Operators from Weighted Bergman Spaces Induced by Doubling Weights into Bloch-Type Spaces"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2051-7253","authenticated-orcid":false,"given":"Xiangling","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Computer Science, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinghua","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Qufu Normal University, Qufu 273100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"55","DOI":"10.2478\/s11533-012-0097-4","article-title":"New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space","volume":"11","author":"Colonna","year":"2013","journal-title":"Cent. 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