Stability of Localized Integral Operators on Normal Spaces of Homogeneous Type

The L-p-stability of linear operators is one of fundamental concepts in many research fields. In this article, we introduce a family of localized integral operators on a normal space of homogeneous type such that their kernels have some off-diagonal decay, mild singularity near the diagonal and certain Holder regularity, and we show that localized integral operators in the family have their L-p-stability to be equivalent for different exponents 1 <= p <= infinity.