Bivariate Koornwinder–Sobolev Orthogonal Polynomials Marriaga, Misael E. Pérez Fernández, Teresa Encarnación Piñar González, Miguel Ángel Bivariate orthogonal polynomials Sobolev orthogonal polynomials Mathematics Subject Classification. 42C05, 33C50. The authors are grateful to the referee for his/her valuable comments and careful reading, which allowed us to improve this paper. The work of the first author (MEM) has been supported by Ministerio de Ciencia, Innovaci´on y Universidades (MICINN) grant PGC2018-096504-B-C33. Second and third authors (TEP and MAP) thank FEDER/Ministerio de Ciencia, Innovaci´on y Universidades—Agencia Estatal de Investigaci´on/PGC2018-094932-B-I00 and Research Group FQM-384 by Junta de Andaluc´ıa. This work is supported in part by the IMAG-Mar´ıa de Maeztu grant CEX2020-001105-M/AEI/10. 13039/501100011033. The so-called Koornwinder bivariate orthogonal polynomials are generated by means of a non-trivial procedure involving two families of univariate orthogonal polynomials and a function ρ(t) such that ρ(t)2 is a polynomial of degree less than or equal to 2. In this paper, we extend the Koornwinder method to the case when one of the univariate families is orthogonal with respect to a Sobolev inner product. Therefore, we study the new Sobolev bivariate families obtaining relations between the classical original Koornwinder polynomials and the Sobolev one, deducing recursive methods in order to compute the coefficients. The case when one of the univariate families is classical is analysed. Finally, some useful examples are given. 2022-02-04T11:11:21Z 2022-02-04T11:11:21Z 2021-10-03 info:eu-repo/semantics/article Marriaga, M.E., Pérez, T.E. & Piñar, M.A. Bivariate Koornwinder–Sobolev Orthogonal Polynomials. Mediterr. J. Math. 18, 234 (2021). [https://doi.org/10.1007/s00009-021-01875-6] http://hdl.handle.net/10481/72667 10.1007/s00009-021-01875-6 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Springer Nature