Abstract
For algebraic polynomial approximation on [−1,1] the analogue of the Zygmund-Timan type converse Marchaud inequality is proved. These are the exact converse estimates inL p spaces when 1<p<∞. The proof forp>2 uses Hirschman's multiplier theory, while forp<−2 we apply an elementary but rather complicated cutting argument.
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Communicated by Ronald A. DeVore.
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Totik, V. Sharp converse theorem ofL p-polynomial approximation. Constr. Approx 4, 419–433 (1988). https://doi.org/10.1007/BF02075471
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DOI: https://doi.org/10.1007/BF02075471