{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T10:47:43Z","timestamp":1778755663755,"version":"3.51.4"},"reference-count":25,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2023,4,8]],"date-time":"2023-04-08T00:00:00Z","timestamp":1680912000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00297\/2020"],"award-info":[{"award-number":["UIDB\/00297\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For  and variable exponents  and  with values in [1, \u221e], let the variable exponents  be defined by\n<jats:disp-formula\/>The Riesz\u2013Thorin\u2013type interpolation theorem for variable Lebesgue spaces says that if a linear operator <jats:italic>T<\/jats:italic> acts boundedly from the variable Lebesgue space  to the variable Lebesgue space  for , then\n<jats:disp-formula\/>where <jats:italic>C<\/jats:italic> is an interpolation constant independent of <jats:italic>T<\/jats:italic>. We consider two different modulars  and  generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants <jats:italic>C<\/jats:italic><jats:sub>max<\/jats:sub> and <jats:italic>C<\/jats:italic><jats:sub>sum<\/jats:sub>, which imply that  and , as well as, lead to sufficient conditions for  and . We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that ,  are Lipschitz continuous and bounded away from one and infinity (in this case, ).<\/jats:p>","DOI":"10.1002\/mana.202100549","type":"journal-article","created":{"date-parts":[[2023,4,9]],"date-time":"2023-04-09T02:35:40Z","timestamp":1681007740000},"page":"2877-2902","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the interpolation constants for variable Lebesgue spaces"],"prefix":"10.1002","volume":"296","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6815-0561","authenticated-orcid":false,"given":"Oleksiy","family":"Karlovych","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es Departamento de Matem\u00e1tica Faculdade de Ci\u00eancias e Tecnologia Universidade Nova de Lisboa, Quinta da Torre  Caparica Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9145-8978","authenticated-orcid":false,"given":"Eugene","family":"Shargorodsky","sequence":"additional","affiliation":[{"name":"Department of Mathematics King's College London Strand London UK"},{"name":"Fakult\u00e4t Mathematik Technische Universit\u00e4t Dresden Dresden Germany"}]}],"member":"311","published-online":{"date-parts":[[2023,4,8]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a\u201020448"},{"key":"e_1_2_7_3_1","doi-asserted-by":"crossref","first-page":"x+207","DOI":"10.1007\/978-3-642-66451-9","volume-title":"Interpolation spaces. An introduction","author":"Bergh J.","year":"1976"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.4064\/sm\u201024\u20102\u2010113\u2010190"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.7153\/mia\u201015\u201056"},{"key":"e_1_2_7_6_1","first-page":"x+312","volume-title":"Applied and Numerical Harmonic Analysis","author":"Cruz\u2010Uribe D. 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Vol. 1, Operator Theory: Advances and Applications","author":"Kokilashvili V.","year":"2016"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.03.012"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.21136\/CMJ.1991.102493"},{"key":"e_1_2_7_16_1","unstructured":"L.Maligranda Orlicz spaces and interpolation Semin\u00e1rios de Matem\u00e1tica [Seminars in Mathematics] vol.5 Universidade Estadual de Campinas Departamento de Matem\u00e1tica Campinas 1989 pp.iii+206."},{"key":"e_1_2_7_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00013\u2010003\u20100512\u2010y"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.02.043"},{"key":"e_1_2_7_19_1","doi-asserted-by":"publisher","DOI":"10.2140\/apde.2019.12.1711"},{"key":"e_1_2_7_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2015.11.013"},{"key":"e_1_2_7_21_1","doi-asserted-by":"publisher","DOI":"10.1080\/17476933.2016.1244190"},{"key":"e_1_2_7_22_1","doi-asserted-by":"publisher","DOI":"10.32917\/hmj\/1544238031"},{"key":"e_1_2_7_23_1","doi-asserted-by":"crossref","first-page":"iii+222","DOI":"10.1007\/BFb0072210","volume-title":"Orlicz spaces and modular spaces","author":"Musielak J.","year":"1983"},{"key":"e_1_2_7_24_1","first-page":"63","volume-title":"On variable Lebesgue spaces","author":"Nguyen P. 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