Before revision:  The choice of 0<p<1 , fits the nature of the constraints to which quadrature rules are subject, thus providing a more suitable formulation for sparse quadrature recovery than the one based on \ell^1-norm minimization.
After revision:  The choice of 0<p<1 , fits the nature of the constraints to which quadrature rules are subject, thus providing a more natural formulation for sparse quadrature recovery than the one based on \ell^1-norm minimization.