Improved $L^p$ bounds for Bochner–Riesz operators associated with rough convex domains in the plane

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2025年3月22日

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Hrit Roy

摘要

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

Improved \(L^p\) bounds for Bochner–Riesz operators associated with rough convex domains in the plane

摘要