Bounds for $L_p$-discrepancies of point distributions in compact metric spaces

Abstract

Upper bounds for the $L_p$-discrepancies of point distributions in compact metric measure spaces for $0<p\le \infty$ have been established in the paper [6] by Brandolini, Chen, Colzani, Gigante and Travaglini. In the present paper we show that such bounds can be established in a much more general situation under very simple conditions on the volume of metric balls as a function of radii.

References in corpus (3)

• Diameter bounded equal measure partitions of Ahlfors regular metric measure spaces
• Stolarsky principle and energy optimization on the sphere
• Point distribution in compact metric spaces, III. Two-point homogeneous spaces