The primary purpose of this paper is to study the Wiener-type regularity
criteria for non-linear equations driven by integro-differential operators,
whose model is the fractional pβLaplace equation. In doing so, with the help
of tools from potential analysis, such as fractional relative Sobolev
capacities, Wiener type integrals, Wolff potentials, (Ξ±,p)βbarriers, and
(Ξ±,p)βbalayages, we first prove the characterizations of the fractional
thinness and the Perron boundary regularity. Then, we establish a Wiener test
and a generalized fractional Wiener criterion. Furthermore, we also prove the
continuity of the fractional superharmonic function, the fractional
resolutivity, a connection between (Ξ±,p)βpotentials and
(Ξ±,p)βPerron solutions, and the existence of a capacitary function for
an arbitrary condenser.Comment: 27 pages, any comments are welcom