On Riesz Type Kernels Over Local Fields

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Abstract

Based on a representation lemma, Riesz type kernels on the local field K and on the integer ring O in K are constructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip (Lr;a) and the Lp boundedness of such operators motivated by the open problem: Does σ n f → a , e f for f ∈ L1(0) (see M. H. Taibleson [6] and [5])?
Original languageAmerican English
JournalApproximation Theory and its Applications
Volume11
DOIs
StatePublished - Dec 1995

Disciplines

  • Mathematics

Keywords

  • Local field
  • Poisson Summation Formula
  • Riesz operator
  • Type kernel
  • Weak type

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