Almost everywhere convergence of nets of operators and weak type maximal inequalities
Volume 262 / 2023
Fundamenta Mathematicae 262 (2023), 287-304
MSC: Primary 42B25; Secondary 28A15, 47A35, 43A50.
DOI: 10.4064/fm272-2-2023
Published online: 11 April 2023
Abstract
The weak type maximal principles of Stein and Sawyer are extended to nets of operators defined on classes of functions on general measure spaces (possibly of infinite measure), including the case of locally compact groups. Applications to differentiation of integrals, multiple Fourier series and multi-parameter ergodic averages are given.
