Almost everywhere convergence for modified Bochner–Riesz means at the critical index for $p \geq 2$

Marco Annoni

Vol. 286 (2017), No. 2, 257–275

DOI: 10.2140/pjm.2017.286.257

Abstract

Boundedness for a maximal modified Bochner–Riesz operator between weighted $L^2$ spaces is proved. As a consequence, we have sufficient conditions for a.e. convergence of the modified Bochner–Riesz means at the critical exponent $p_{\lambda }^{}=2n∕\left(n-2\lambda -1\right)$.

Keywords

Bochner–Riesz means, maximal Bochner–Riesz means, almost everywhere convergence, weighted inequalities, radial multipliers

Mathematical Subject Classification 2010

Primary: 42B15

Secondary: 42B10, 42B25

Milestones

Received: 4 November 2014

Accepted: 26 June 2016

Published: 15 January 2017