Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Beltran, DavidRoos, JorisSeeger, Andreas2024-10-172024-10-172023https://oa.tib.eu/renate/handle/123456789/16985https://doi.org/10.34657/16007We consider Bochner-Riesz means on weighted Lp spaces, at the critical index λ(p)=d(1/p−1/2)−1/2. For every A₁-weight we obtain an extension of Vargas' weak type (1,1) inequality in some range of p>1. To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension d=2; partial results as well as conditional results are proved in higher dimensions. For the means of index λ∗=(d−1)/(2d+2) we prove fully optimal sparse bounds.engBochner-Riesz MeansSparse DominationEndpoint EstimatesWeighted Norm EstimatesConvergence in Weighted Spaces510Report