Abstract:
We consider sequences of operators $U_n\colon L^1(X)\to M(X)$, where $X$ is a space of homogeneous type. Under some conditions on the operators $U_n$ we give a complete characterization of convergence (divergence) sets of sequences of functions $U_n(f)$, where $f\in L^p(X)$, $1\le p\le \infty$. The results are applied to characterize the convergence sets of some specific operator sequences in classical analysis.
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