On pointwise convergence of linear integral operators with homogeneous kernels

Abstract

Here we give some approximation theorems concerning pointwise convergence and rate of pointwise convergence for non-convolution type linear operators of the form:

with kernels satisfying some general homogeneity assumptions. Here Λ is a non-empty set of indices with a topology and λ₀ an accumulation point of Λ in this topology.

Keywords:

• pointwise convergence
• rate of convergence
• linear singular integral operators
• Lebesgue points
• homogeneity

AMS Subject Classifications:

• 41A35
• 41A25
• 47G10

Acknowledgements

The authors want to thank Prof. P.L. Butzer for the useful suggestions in the matter.