On differentiation of integrals in the infinite-dimensional torus. (English) Zbl 1466.43004
Summary: We answer the recently posed questions regarding the problem of differentiation of integrals for the Rubio de Francia basis \(\mathcal{R}\) in the infinite torus \(\mathbb{T}^\omega\). In particular, we prove that \(\mathcal{R}\) does not differentiate \(L^\infty(\mathbb{T}^\omega)\). Some remarks about differentiation in the context of arbitrary bases are also included.
MSC:
| 43A75 | Harmonic analysis on specific compact groups |
| 42B25 | Maximal functions, Littlewood-Paley theory |
Keywords:
infinite-dimensional torus; differentiation of integrals; differentiation basis; maximal operatorReferences:
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