{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:12:05Z","timestamp":1762956725769,"version":"3.45.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Z. Anal. Anwend."],"published-print":{"date-parts":[[2010,6,23]]},"abstract":"<jats:p>\n                    We determine the trace of Besov spaces\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathfrak B^s_{p,q}(\\mathbb R^n)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and Triebel\u2013Lizorkin  spaces\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathfrak F^s_{p,q}(\\mathbb R_n)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    \u2013 characterized via atomic decompositions \u2013 on hyperplanes\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbb R^m<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>n&gt;m \\in \\mathbb N<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , for parameters\n                    <jats:inline-formula>\n                      <jats:tex-math>0 &lt; p, q \\leq \\infty<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>s &gt; \\frac{n\u2212m}p<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . The limiting case\n                    <jats:inline-formula>\n                      <jats:tex-math>s = \\frac{n\u2212m}p<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is investigated as well. Our results remain valid considering the classical spaces\n                    <jats:inline-formula>\n                      <jats:tex-math>\\bm B^s_{p,q}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>\\bm F^s_{p,q}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    \u2013 de\ufb01ned via differences. Finally, we include some density assertions, which imply that the trace does not exist when\n                    <jats:inline-formula>\n                      <jats:tex-math>s&lt;\\frac{n\u2212m}p<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.4171\/zaa\/1409","type":"journal-article","created":{"date-parts":[[2010,6,23]],"date-time":"2010-06-23T17:49:52Z","timestamp":1277315392000},"page":"275-302","source":"Crossref","is-referenced-by-count":17,"title":["Trace Operators in Besov and Triebel\u2013Lizorkin Spaces"],"prefix":"10.4171","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2448-3724","authenticated-orcid":false,"given":"Cornelia","family":"Schneider","sequence":"first","affiliation":[{"name":"Universidade de Coimbra, Portugal"}]}],"member":"2673","container-title":["Zeitschrift f\u00fcr Analysis und ihre Anwendungen"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/ZAA\/1409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:03:22Z","timestamp":1762956202000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/zaa\/1409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,23]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/zaa\/1409","relation":{},"ISSN":["0232-2064","1661-4534"],"issn-type":[{"type":"print","value":"0232-2064"},{"type":"electronic","value":"1661-4534"}],"subject":[],"published":{"date-parts":[[2010,6,23]]}}}