{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T16:47:35Z","timestamp":1709657255622},"reference-count":11,"publisher":"Wiley","issue":"5-6","license":[{"start":{"date-parts":[[2011,3,14]],"date-time":"2011-03-14T00:00:00Z","timestamp":1300060800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2011,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We determine the trace of Besov spaces <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$\\mathfrak {B}^s_{p,q}(\\Omega )$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content> and Triebel\u2010Lizorkin spaces <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$\\mathfrak {F}^s_{p,q}(\\Omega )$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-2.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>, characterized via atomic decompositions, on the boundary of <jats:italic>C<jats:sup>k<\/jats:sup><\/jats:italic> domains \u03a9 for parameters 0 &lt; <jats:italic>p<\/jats:italic>, <jats:italic>q<\/jats:italic> \u2a7d \u221e and <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$s&gt;\\frac{1}{p}$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-3.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>. The limiting case <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$s=\\frac{1}{p}$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-4.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content> is investigated as well. In terms of Besov spaces our results remain valid for the classical spaces <jats:bold>B<\/jats:bold><jats:sup><jats:italic>s<\/jats:italic><\/jats:sup><jats:sub><jats:italic>p<\/jats:italic>,<jats:italic>q<\/jats:italic><\/jats:sub>(\u03a9) defined via differences. Furthermore, we include some density assertions, which imply that the trace does not exist when <jats:styled-content>\\documentclass{article}\\usepackage{amssymb}\\pagestyle{empty}\\begin{document}$s&lt;\\frac{1}{p}$\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-5.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>. \u00a9 2011 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim<\/jats:p>","DOI":"10.1002\/mana.201010052","type":"journal-article","created":{"date-parts":[[2011,3,14]],"date-time":"2011-03-14T08:12:05Z","timestamp":1300090325000},"page":"572-586","source":"Crossref","is-referenced-by-count":10,"title":["Traces of Besov and Triebel\u2010Lizorkin spaces on domains"],"prefix":"10.1002","volume":"284","author":[{"given":"Cornelia","family":"Schneider","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,3,14]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2154408"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1985.34.34041"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2008.12.004"},{"issue":"882","key":"e_1_2_5_5_1","first-page":"97","article-title":"An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation","volume":"188","author":"Hedberg L. 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