Fractional calculus for power functions
  We calculate the fractional Laplacian for functions of the form $u(x)=(1-|x|^2)_+^p$ and $v(x)=x_d u(x)$. As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball. 
Bart{\l}omiej Dyda
math.AP math.PR