Orthogonal exponentials on the generalized plane Sierpinski gasket

The self-affine measure μMp,D corresponding toMp=2p02(p∈Z)andD=00,10,01is supported on the the generalized plane Sierpinski gasket T(Mp,D). In the present paper we show that there exist at most 3 mutually orthogonal exponential functions in L2(μMp,D), and the number 3 is the best. This generalizes several known results on the non-spectral self-affine measure problem.