On the convergence sets of operator sequences on spaces of homogeneous type
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918236935684096 |
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| author | Karagulyan, Grigori A. |
| author_facet | Karagulyan, Grigori A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the convergence sets of operator sequences on spaces of homogeneous type Karagulyan, Grigori A. Classical Analysis and ODEs General Topology 42A20, 40A30 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. |
| title | On the convergence sets of operator sequences on spaces of homogeneous type |
| topic | Classical Analysis and ODEs General Topology 42A20, 40A30 |
| url | https://arxiv.org/abs/2310.00621 |