Irregularities of Distribution on Two-Point Homogeneous Spaces

We study the irregularities of distribution on two-point homogeneous spaces. Our main result is the following: let d be the real dimension of a two point homogeneous space, let {aj}j=1N,{xj}j=1N be a system of positive weights and points on and let (Forumala presented). be the discrepancy associated with the ball Br(x). Then, if d1(mod4), for any radius 0<r<π∕2, we obtain the sharp estimate ∫Dr(x)2+D2r(x)2dμ(x)cN−1−1d.