Orthogonal exponentials on the generalized plane Sierpinski gasket

The self-affine measure μ_Mp,D corresponding tois supported on the the generalized plane Sierpinski gasket T(M_p,D). In the present paper we show that there exist at most 3 mutually orthogonal exponential functions in L²(μ_Mp,D), and the number 3 is the best. This generalizes several known results on the non-spectral self-affine measure problem.