Migliorati, Giovanni2014-11-112014-11-112014-11-11201510.1016/j.jat.2014.10.010https://infoscience.epfl.ch/handle/20.500.14299/108567WOS:000347600400010We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is expanded in series of tensorized Legendre or Chebyshev or Gegenbauer or Jacobi orthogonal polynomials indexed by a downward closed multi-index set. The proofs of these inequalities rely on a general result concerning the summation of tensorized polynomials over arbitrary downward closed multi-index sets.Approximation theoryMultivariate polynomial approximationMarkov inequalityNikolskii inequalityOrthogonal polynomialsDownward closed setsLegendre polynomialsChebyshev polynomialsJacobi polynomialsGegenbauer polynomialstext::journal::journal article::research article