Regularity of invariant distributions
Abstract
Description
We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in terms of the conformal weight, the Hausdorff dimension of the limit set, and the maximal rank of the cusps of the group.
58 pages; corrected version - The main theorem of the previous version was incorrect in the case that the invariant distribution is not a cusp form. We thank W. Schmid for showing us a counterexample to this wrong claim
58 pages; corrected version - The main theorem of the previous version was incorrect in the case that the invariant distribution is not a cusp form. We thank W. Schmid for showing us a counterexample to this wrong claim