{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,11,13]],"date-time":"2022-11-13T15:26:22Z","timestamp":1668353182314},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p> Let T be a Calder\u00f3n\u2013Zygmund operator on Heisenberg group \u210d<jats:sup>d<\/jats:sup>. In this paper, by wavelets, we introduce a class of pseudo-annular operators {T<jats:sub>R<\/jats:sub>}<jats:sub>R\u22651<\/jats:sub> to decompose T. By controlling the bandwidth of T<jats:sub>R<\/jats:sub>, we could obtain the approximate rate of T from L<jats:sup>2<\/jats:sup>(\u210d<jats:sup>d<\/jats:sup>) to L<jats:sup>2<\/jats:sup>(\u210d<jats:sup>d<\/jats:sup>) at an ideal rate. <\/jats:p>","DOI":"10.1142\/s0219691315500010","type":"journal-article","created":{"date-parts":[[2014,12,11]],"date-time":"2014-12-11T08:41:31Z","timestamp":1418287291000},"page":"1550001","source":"Crossref","is-referenced-by-count":1,"title":["Pseudo-annular decomposition and approximate rate of Calder\u00f3n\u2013Zygmund operators on Heisenberg group"],"prefix":"10.1142","volume":"13","author":[{"given":"Pengtao","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics, Qingdao University, Qingdao, Shandong 266071, P. R. China"}]},{"given":"Heping","family":"Liu","sequence":"additional","affiliation":[{"name":"LMAM School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"}]},{"given":"Lizhong","family":"Peng","sequence":"additional","affiliation":[{"name":"LMAM School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"}]},{"given":"Qixiang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statics, Wuhan University, Wuhan 430072, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2015,3,9]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.4171\/RMI\/17"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02871663"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-006-6002-4"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-05-08108-6"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/10020070512331342620"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0252-9602(09)60102-8"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1997.180.101"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691310003328"},{"key":"rf9","volume-title":"Ondelettes et Op\u00e9rateurs, I et II","author":"Meyer Y.","year":"1992"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530508001055"},{"key":"rf11","unstructured":"L.\u00a0Peng, Geometry and Nonlinear Partial Differential Equations, AMS\/IP Studies in Advanced Mathematics\u00a029 (American Mathematical Society, 2002)\u00a0pp. 123\u2013131."},{"key":"rf12","first-page":"438","volume":"50","author":"Semmes S.","year":"2003","journal-title":"Notices Amer. Math. Soc."},{"key":"rf13","first-page":"640","volume":"50","author":"Semmes S.","year":"2003","journal-title":"Notices Amer. Math. Soc."},{"key":"rf14","volume-title":"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals","author":"Stein E. M.","year":"1993"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(91)90066-E"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1996.0011"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691315500010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:04:37Z","timestamp":1565118277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691315500010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":16,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2015,3,9]]},"published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1142\/S0219691315500010"],"URL":"https:\/\/doi.org\/10.1142\/s0219691315500010","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}