The Fatou Property for General Approximate Identities on Metric Measure Spaces

approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of approximate identities occurs almost everywhere for functions from the spaces , . The results are illustrated with examples of Poisson kernel...

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Veröffentlicht in:Mathematical Notes 2021-07, Vol.110 (1-2), p.196-209
Hauptverfasser: Karagulyan, G. A., Katkovskaya, I. N., Krotov, V. G.
Format: Artikel
Sprache:eng
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Zusammenfassung:approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of approximate identities occurs almost everywhere for functions from the spaces , . The results are illustrated with examples of Poisson kernels and their powers in the unit ball in or , and also of convolutions with dilatations on . In all these examples, the conditions found are exact.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S000143462107021X