Constructive Approximation

, Volume 24, Issue 1, pp 91-112

First online:

Jackson-Type Inequality for Doubling Weights on the Sphere

  • Feng DaiAffiliated withDepartment of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1 Email author 

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In the one-dimensional case, Jackson's inequality and its converse for weighted algebraic polynomial approximation, as well as many important, weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc., have been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumption on the weights. In most cases this minimal assumption is the doubling condition. In this paper, we establish Jackson's theorem and its Stechkin-type converse for spherical polynomial approximation with respect to doubling weights on the unit sphere.

Moduli of smoothness Best approximation by spherical polynomials Spherical harmonics Jackson's inequality Doubling weights