On the sweeping out property for convolution operators of discrete measures

G. A. Karagulyan
2010 Proceedings of the American Mathematical Society  
Let μ n be a sequence of discrete measures on the unit circle T = R/Z with μ n (0) = 0, and μ n ((−δ, δ)) → 1, as n → ∞. We prove that the sequence of convolution operators (f * μ n )(x) is strong sweeping out; i.e., there exists a set E ⊂ T such that lim sup almost everywhere on T.
doi:10.1090/s0002-9939-2010-10829-8 fatcat:qykh6dth2zawdjdfobanqy2f5e