Weighted Sobolev spaces: Markov-type inequalities and duality

Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. The aim of this paper is to prove several important properties of weighted Sobolev spaces: separability, reflexivity, uniform convexity, duality and Markov-type inequalities.Francisco Marcellán: Supported in part by two Grants from Ministerio de Economía y Competitividad (MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P), Spain. Yamilet Quintana: Supported in part by a Grant from Ministerio de Economía y Competitividad (MTM2012-36732-C03-01), Spain. José M. Rodríguez: Supported in part by three Grants from Ministerio de Economía y Competititvidad, Agencia Estatal de Investigacin (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2013-46374-P, MTM2016-78227-C2-1-P and MTM2015-69323-REDT), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México