{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T15:40:07Z","timestamp":1719070807209},"reference-count":39,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,5,12]],"date-time":"2008-05-12T00:00:00Z","timestamp":1210550400000},"content-version":"vor","delay-in-days":132,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Ghent University","award":["01T13804"]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2008,1]]},"abstract":"Let be the space of s<\/jats:italic>\u2010vectors (0 \u2264 s<\/jats:italic> \u2264 m<\/jats:italic> + 1) in the Clifford\nalgebra \u211d<\/jats:italic>0,m<\/jats:italic>+1<\/jats:sub> constructed over the quadratic vector space \u211d<\/jats:italic>0,m<\/jats:italic>+1<\/jats:sup>, let r<\/jats:italic>, p<\/jats:italic>, q<\/jats:italic> \u2208 \u2115<\/jats:italic> with 0 \u2264 r<\/jats:italic> \u2264 m<\/jats:italic> + 1, \u2009<\/jats:italic>0 \u2264 p<\/jats:italic> \u2264 q<\/jats:italic>, and r<\/jats:italic> + 2q<\/jats:italic> \u2264 m<\/jats:italic> + 1, and let . Then, an \u2010valued smooth function W<\/jats:italic> defined in an open subset \u03a9<\/jats:italic> \u2282 \u211d<\/jats:italic>m<\/jats:italic>+1<\/jats:sup> is said to satisfy the generalized\nMoisil\u2010Th\u00e9odoresco system of type (r<\/jats:italic>, p<\/jats:italic>, q<\/jats:italic>) if \u2202<\/jats:italic>x<\/jats:italic><\/jats:sub>W<\/jats:italic> = 0 in \u03a9<\/jats:italic>, where \u2202<\/jats:italic>x<\/jats:italic><\/jats:sub> is the Dirac operator in \u211d<\/jats:italic>m<\/jats:italic>+1<\/jats:sup>. A structure theorem is proved\nfor such functions, based on the construction of conjugate harmonic\npairs. Furthermore, if \u03a9<\/jats:italic> is bounded with boundary \u0393<\/jats:italic>, where \u0393<\/jats:italic> is\nan Ahlfors\u2010David regular surface, and if W<\/jats:italic> is a \u2010valued H\u00f6lder\ncontinuous function on \u0393<\/jats:italic>, then necessary and sufficient conditions are\ngiven under which W<\/jats:italic> admits on \u0393<\/jats:italic> a Cauchy integral decomposition\nW<\/jats:italic> = W<\/jats:italic>+<\/jats:sub> + W<\/jats:italic>\u2212<\/jats:sub>.<\/jats:p>","DOI":"10.1155\/2008\/746946","type":"journal-article","created":{"date-parts":[[2008,5,15]],"date-time":"2008-05-15T14:19:33Z","timestamp":1210861173000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Generalized Moisil\u2010Th\u00e9odoresco Systems and Cauchy Integral Decompositions"],"prefix":"10.1155","volume":"2008","author":[{"given":"Ricardo","family":"Abreu Blaya","sequence":"first","affiliation":[]},{"given":"Juan","family":"Bory Reyes","sequence":"additional","affiliation":[]},{"given":"Richard","family":"Delanghe","sequence":"additional","affiliation":[]},{"given":"Frank","family":"Sommen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,5,12]]},"reference":[{"key":"e_1_2_7_1_2","volume-title":"Analysis. 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