{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T21:06:22Z","timestamp":1648760782437},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,3,15]],"date-time":"2015-03-15T00:00:00Z","timestamp":1426377600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Integr. Equ. Oper. Theory"],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1007\/s00020-015-2225-6","type":"journal-article","created":{"date-parts":[[2015,3,14]],"date-time":"2015-03-14T05:23:58Z","timestamp":1426310638000},"page":"249-265","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Hilbert\u2013Schmidt Norm of Hankel Operators on Poly-Bergman Spaces"],"prefix":"10.1007","volume":"82","author":[{"given":"Lu\u00eds V.","family":"Pessoa","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,3,15]]},"reference":[{"key":"2225_CR1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s00020-012-1956-x","volume":"73","author":"L.D. Abreu","year":"2012","unstructured":"Abreu L.D.: Super-wavelets versus poly-Bergman spaces. Integral Equ. Oper. Theory 73, 177\u2013193 (2012)","journal-title":"Integral Equ. Oper. Theory"},{"key":"2225_CR2","first-page":"179","volume":"406","author":"J. Arazy","year":"1990","unstructured":"Arazy J., Fisher S.D., Janson S., Peetre J.: An identity for reproducing kernels in a planar domain and Hilbert\u2013Schmidt Hankel Operators. J. Reine Angew. Math. 406, 179\u2013199 (1990)","journal-title":"J. Reine Angew. Math."},{"key":"2225_CR3","volume-title":"Polyanalytic Functions","author":"M.B. Balk","year":"1991","unstructured":"Balk M.B.: Polyanalytic Functions. Akademie Verlag, Berlin (1991)"},{"key":"2225_CR4","first-page":"191","volume":"549","author":"H. Begehr","year":"2002","unstructured":"Begehr H.: Orthogonal decompositions of the function space $${L^2(\\bar{D}; \\mathbb{C})}$$ L 2 ( D \u00af \u037e C ) . J. Reine Angew. Math. 549, 191\u2013219 (2002)","journal-title":"J. Reine Angew. Math."},{"key":"2225_CR5","first-page":"1193","volume":"79","author":"C.A. Berger","year":"1973","unstructured":"Berger C.A., Shaw B.I.: Selfcommutators of multicyclic hypornormal operators are always trace class. Proc. Am. Math. Soc. 79, 1193\u20131199 (1973)","journal-title":"Proc. Am. Math. Soc."},{"key":"2225_CR6","doi-asserted-by":"crossref","unstructured":"Berger, C., Shaw, B.: Intertwining, analytic structures, and the trace norm estimate. In: Proceedings of a Conference in Operator Theory. Springer Lecture Notes in Mathematics, vol. 345, pp. 1\u20136 (1973)","DOI":"10.1007\/BFb0058914"},{"key":"2225_CR7","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/005","volume-title":"The Kernel Function and Conformal Mapping","author":"S. Bergman","year":"1950","unstructured":"Bergman S.: The Kernel Function and Conformal Mapping. American Mathematical Society, New York (1950)"},{"key":"2225_CR8","doi-asserted-by":"crossref","first-page":"277","DOI":"10.4153\/CJM-2004-013-8","volume":"56","author":"M.R. Dostanic","year":"2004","unstructured":"Dostanic M.R.: Spectral properties of the commutator of Bergman\u2019s projection and the operator of multiplication by an analytic function. Can. J. Math. 56, 277\u2013292 (2004)","journal-title":"Can. J. Math."},{"key":"2225_CR9","first-page":"251","volume":"32","author":"A. Dzhuraev","year":"1985","unstructured":"Dzhuraev A.: The polykernel function of a domain, kernel operators, and singular integral operators. Sov. Math. Dokl. 32, 251\u2013253 (1985)","journal-title":"Sov. Math. Dokl."},{"key":"2225_CR10","volume-title":"Methods of Singular Integral equations","author":"A. Dzhuraev","year":"1992","unstructured":"Dzhuraev A.: Methods of Singular Integral equations. Longman Scientific & Technical, Harlow (1992)"},{"key":"2225_CR11","volume-title":"Partial Differential Equations","author":"A. Friedman","year":"1969","unstructured":"Friedman A.: Partial Differential Equations. Holt, Rinehart and Winston, New York (1969)"},{"key":"2225_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-12245-3","volume-title":"Polyharmonic Boundary Value Problems","author":"F. Gazzola","year":"2010","unstructured":"Gazzola F., Grunau H.C., Sweers G.: Polyharmonic Boundary Value Problems. Springer, Berlin (2010)"},{"key":"2225_CR13","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1080\/17476933.2011.629724","volume":"57","author":"Y.I. Karlovich","year":"2012","unstructured":"Karlovich Y.I., Mozel V.A.: C*-algebras of Bergman-type operators with piecewise continuous coefficients and shifts. Complex Var. Elliptic Equ. 57, 841\u2013865 (2012)","journal-title":"Complex Var. Elliptic Equ."},{"key":"2225_CR14","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s00020-006-1473-x","volume":"57","author":"Y.I. Karlovich","year":"2007","unstructured":"Karlovich Y.I., Pessoa L.V.: C*-algebras of Bergman type operators with piecewise continuous coefficients. Integral Equ. Oper. Theory 57, 521\u2013565 (2007)","journal-title":"Integral Equ. Oper. Theory"},{"key":"2225_CR15","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/978-3-7643-8684-9_12","volume":"181","author":"Y.I. Karlovich","year":"2008","unstructured":"Karlovich Y.I., Pessoa L.V.: Poly-Bergman projections and orthogonal decompositions of L 2-spaces over bounded domains. Oper. Theory Adv. Appl. 181, 263\u2013282 (2008)","journal-title":"Oper. Theory Adv. Appl."},{"key":"2225_CR16","first-page":"277","volume":"232","author":"A.D. Koshelev","year":"1977","unstructured":"Koshelev A.D.: On the kernel function of the Hilbert space of functions polyanalytic in a disc. Dokl. Akad. Nauk. SSSR [Soviet Math. Dokl.] 232, 277\u2013279 (1977)","journal-title":"Dokl. Akad. Nauk. SSSR [Soviet Math. Dokl.]"},{"key":"2225_CR17","first-page":"329","volume":"233","author":"A.D. Koshelev","year":"1977","unstructured":"Koshelev A.D.: An application of polyharmonic functions in the theory of elasticity. Dokl. Akad. Nauk. SSSR [Soviet Phys. Dokl.] 233, 329\u2013331 (1977)","journal-title":"Dokl. Akad. Nauk. SSSR [Soviet Phys. Dokl.]"},{"key":"2225_CR18","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s11785-012-0268-0","volume":"8","author":"L.V. Pessoa","year":"2014","unstructured":"Pessoa L.V.: Planar Beurling transform and Bergman type spaces. Complex Anal. Oper. Theory 8, 359\u2013381 (2014)","journal-title":"Complex Anal. Oper. Theory"},{"key":"2225_CR19","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s11785-010-0119-9","volume":"7","author":"L.V. Pessoa","year":"2013","unstructured":"Pessoa L.V.: Dzhuraev\u2019s formulas and poly-Bergman kernels on domains M\u00f6bius equivalent to a disk. Complex Anal. Oper. Theory 7, 193\u2013220 (2013)","journal-title":"Complex Anal. Oper. Theory"},{"issue":"18","key":"2225_CR20","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1002\/mana.201010057","volume":"17","author":"L.V. Pessoa","year":"2013","unstructured":"Pessoa L.V.: The method of variation of the domain on poly-Bergman spaces. Math. Nachr. 17(18), 1850\u20131862 (2013)","journal-title":"Math. Nachr."},{"key":"2225_CR21","doi-asserted-by":"crossref","first-page":"1350042 (23 pag","DOI":"10.1142\/S0129167X13500420","volume":"24","author":"L.V. Pessoa","year":"2013","unstructured":"Pessoa L.V.: Toeplitz operators and the essential boundary on polyanalytic functions. Int. J. Math. 24, 1350042 (23 pages) (2013)","journal-title":"Int. J. Math."},{"key":"2225_CR22","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1016\/j.cam.2007.12.009","volume":"222","author":"A. Torre","year":"2008","unstructured":"Torre A.: Generalized Zernike or disc polynomials: an application in quantum optics. J. Comput. Appl. Math. 222, 622\u2013644 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"2225_CR23","volume-title":"New Methods for Solving Elliptic Equations","author":"I.N. Vekua","year":"1967","unstructured":"Vekua I.N.: New Methods for Solving Elliptic Equations. North-Holland Publishing Co., The Netherlands (1967)"},{"key":"2225_CR24","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/BF01291838","volume":"33","author":"N.L. Vasilevski","year":"1999","unstructured":"Vasilevski N.L.: On the structure of Bergman and poly Bergman spaces. Integral Equ. Oper. Theory 33, 471\u2013488 (1999)","journal-title":"Integral Equ. Oper. Theory"},{"key":"2225_CR25","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/978-3-7643-7980-3_16","volume":"171","author":"N.L. Vasilevski","year":"2007","unstructured":"Vasilevski N.L.: Poly-Bergman spaces and two-dimensional singular integral operators. Oper. Theory Adv. Appl. 171, 349\u2013359 (2007)","journal-title":"Oper. Theory Adv. Appl."},{"key":"2225_CR26","volume-title":"Commutative Algebras of Toeplitz Operators on the Bergman Space","author":"N.L. Vasilevski","year":"2008","unstructured":"Vasilevski N.L.: Commutative Algebras of Toeplitz Operators on the Bergman Space. Birkh\u00e4user, Basel (2008)"},{"key":"2225_CR27","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.cam.2004.04.004","volume":"174","author":"A. W\u00fcnsche","year":"2005","unstructured":"W\u00fcnsche A.: Generalized Zernike or disc polynomials. J. Comput. Appl. Math. 174, 135\u2013163 (2005)","journal-title":"J. Comput. Appl. Math."},{"key":"2225_CR28","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/BF01301468","volume":"40","author":"K. Zhu","year":"2001","unstructured":"Zhu K.: A trace formula for multiplication operators on invariant subspaces of the Bergman space. Integral Equ. Oper. Theory 40, 244\u2013255 (2001)","journal-title":"Integral Equ. Oper. Theory"}],"container-title":["Integral Equations and Operator Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00020-015-2225-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00020-015-2225-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00020-015-2225-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T00:34:00Z","timestamp":1566434040000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00020-015-2225-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,15]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["2225"],"URL":"https:\/\/doi.org\/10.1007\/s00020-015-2225-6","relation":{},"ISSN":["0378-620X","1420-8989"],"issn-type":[{"value":"0378-620X","type":"print"},{"value":"1420-8989","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,15]]}}}