Weighted Polynomial Inequalities with Doubling and A∞ Weights

By G. Mastroianni, Vilmos Totik. 2000

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Polynomial approximation on the sphere using scattered data (2008, methodology): “These inequalities were already proved by Mhaskar, Narcowich, and Ward [6], using the delayed–mean operators by Stein [9], and applying some inequalities with doubling weights by Mastroianni and Totik [5].”
Multivariate polynomial inequalities with respect to doubling weights and A∞ weights (2006, background): “Following [13], we set w0(x) = w1(x) and wn(x) = nd−1 ∫”
Approximation by trigonometric polynomials in weighted Orlicz spaces (2006, background): “More general doubling weights, approximation by trigonometric polynomials in the periodic case and other related problems were studied in [29], [30], [31], [7].”
A Sharp Remez Inequality for Trigonometric Polynomials (2013, unknown): “, [15]).”
Net Spaces and Boundedness of Integral Operators (2011, unknown): “As applications of this result, we obtain the sharp increase rate for the norm of the Cesàro operator from Lp(|x|γ ) into Lq(|x|−β) and a weighted version of the Nikol’skii inequality for trigonometric polynomials (see also [29]).”
Orthogonal polynomials (2005, unknown): “Often only a rough estimate is needed for Christoffel functions, and such a one is provided in Mastroianni–Totik [56]: if μ is supported on [−1, 1] and it is a doubling measure, i.”