Behavior of eigenvalues of certain Schrodinger operators in the rational Dunkl setting

For a normalized root system R in RN and a multiplicity function k >= 0 let N=N+Sigma alpha is an element of Rk(alpha). We denote by dw(x)=Pi alpha is an element of R|x,alpha |k(alpha) dx the associated measure in RN. Let L=-Delta +V, V >= 0, be the Dunkl-Schrodinger operator on RN. Assume that there exists q>max(1,<mml:mfrac>N2</mml:mfrac>) such that V belongs to the reverse Holder class RHq(dw). For lambda >0 we provide upper and lower estimates for the number of eigenvalues of L which are less or equal to lambda. Our main tool in the Fefferman-Phong type inequality in the rational Dunkl setting.