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arXiv · 1210.1956

On the sweeping out property for convolution operators of discrete measures

G. A. Karagulyan
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Abstract

Let $\mu_n$ be a sequence of discrete measures on the unit $\ZT=\ZR/\ZZ$ with $\mu_n(0)=0$, and $\mu_n((-\delta,\delta))\to 1$, as $n\to\infty$. We prove that the sequence of convolution operators $(f\ast\mu_n)(x)$ is strong sweeping out, i.e. there exists a set $E\subset\ZT$ such that \md0 \lim\sup_{n\to\infty}(\ZI_E\ast\mu_n)(x)= 1,\quad \lim\inf_{n\to\infty}(\ZI_E\ast\mu_n)(x)= 0, \emd almost everywhere on $\ZT$.

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G. A. Karagulyan. 2012-10-06. On the sweeping out property for convolution operators of discrete measures. https://doi.org/10.1090/s0002-9939-2010-10829-8

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