Vol. 111, No. 2, 1984

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An interpolation theorem and its applications to positive operators

Vilmos Totik

Vol. 111 (1984), No. 2, 447–481
Abstract

We answer a special case of a problem of Z. Ditzian. The obtained estimate for the Peetre K functional is applied to the characterization of functions for which Tnf f= O(nα) (0 < α < 1), where Tn is either the Bernstein, Szász-Mirakjan or Baskakov operator or their Kantorovich-invariant and ∥⋅∥ denotes either the Lp (p 1) or the supremum norm.

Mathematical Subject Classification 2000
Primary: 41A27
Secondary: 46M35
Milestones
Received: 21 July 1982
Published: 1 April 1984
Authors
Vilmos Totik