Abstract
In this paper, we study the regularity of positive solutions to an integral system associated with Bessel potentials. It is a natural extension of the work of Chen, Li, and Ma in which regularity of solutions to a system of Wolff potentials was proved by using the method of regularity lifting. We will fully use the decay estimate for the Bessel kernel both at the origin and the infinity. This integral system is of independent interest since it coincides with the famous Schrödinger type system of two semi-linear fractional partial differential equations.
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