Stability of Localized Integral Operators on Weighted $L^p$ spaces

Details Stability of Localized Integral Operators on Weighted $L^p$ spaces Stability of Localized Integral Operators on Weighted $L^p$ spaces

2011-07-09

arxiv.org/abs/1107.1818v1

Mathematics

Functional Analysis

Scientific paper

In this paper, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Holder regularity and decay off the diagonal. Our model example is the Bessel potential operator ${\mathcal J}_\gamma, \gamma>0$. We show that if such a localized integral operator has stability on a weighted function space $L^p_w$ for some $p\in [1, \infty)$ and Muckenhoupt $A_p$-weight $w$, then it has stability on weighted function spaces $L^{p'}_{w'}$ for all $1\le p'<\infty$ and Muckenhoupt $A_{p'}$-weights $w'$.

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