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arXiv · 2310.00621

On the convergence sets of operator sequences on spaces of homogeneous type

Grigori A. Karagulyan
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Abstract

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

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Grigori A. Karagulyan. 2023-10-01. On the convergence sets of operator sequences on spaces of homogeneous type. https://doi.org/10.4213/sm10033e

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