  We consider generalized Bochner-Riesz operators associated with planar convex
domains. We construct domains which yield improved $L^p$ bounds for the
Bochner-Riesz over previous results of Seeger-Ziesler and Cladek. The
constructions are based on the existence of large $B_m$ sets due to
Bose-Chowla, and large $\Lambda(p)$ sets due to Bourgain.
