#### Vol. 286, No. 2, 2017

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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
##### 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