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This translates into different regularity properties of local solutions to such equations. Specific applications of the abstract results to the 2D surface quasi-geostrophic equation or the fractional chemotaxis system are presented.<\/jats:p>","DOI":"10.1007\/s00245-023-10019-z","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T09:02:15Z","timestamp":1686301335000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Evolution Equations with Sectorial Operator on Fractional Power Scales"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2245-2916","authenticated-orcid":false,"given":"Rados\u0142aw","family":"Czaja","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4294-0503","authenticated-orcid":false,"given":"Tomasz","family":"D\u0142otko","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"10019_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-9221-6","volume-title":"Linear and Quasilinear Parabolic Problems","author":"H Amann","year":"1995","unstructured":"Amann, H.: Linear and Quasilinear Parabolic Problems, vol. 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