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

G. A. Karagulyan

Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1065-1090

Résumé

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. Bibliography: 44 titles.

Détail

Keywords: operator sequences, spaces of homogeneous type
Mots-clés : convergence sets, divergence sets, quasi-distance.

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