Stability of Localized Integral Operators on Weighted<i>L</i>^<i>p</i>Spaces

Abstract

In this article, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Hölder regularity and decay off the diagonal. Our model example is the Bessel potential operator 𝒥γ, γ > 0. We show that if such a localized integral operator has stability on a weighted function space for some p ∈ [1, ∞) and Muckenhoupt A p -weight w, then it has stability on weighted function spaces and Muckenhoupt A p′-weights w′ for all p′ ∈ [1, ∞).