Integral representation of solutions using Green function for fractional Hardy equations

Abstract

Our main aim is to study Green function for the fractional Hardy operator P := (-Delta)(s) - theta/vertical bar x vertical bar(2s) in R-N, where 0 < theta< Lambda(Ns) and Lambda(N,s) is the best constant in the fractional Hardy inequality. Using Green function, we also show that the integral representation of the weak solution holds.