Abstract
This is an ultimate completion of our earlier paper [3] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were investigated under certain restrictions on the underlying parameters of type. In the present article we take advantage of very recent results due to Nowak, Sjögren and Szarek to fully release those restrictions, and also to provide shorter and more transparent proofs of the previous restricted results. Moreover, we also study mapping properties of analogous operators in the parallel context of symmetrized Jacobi function expansions. Furthermore, as a consequence of our main results we conclude some new results related to the classical non-symmetrized Jacobi polynomial and function expansions.
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Research supported by the National Science Centre of Poland, project no. 2013/09/N/ST1/04120.
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Langowski, B. Harmonic analysis operators related to symmetrized Jacobi expansions for all admissible parameters. Acta Math. Hungar. 150, 49–82 (2016). https://doi.org/10.1007/s10474-016-0652-8
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DOI: https://doi.org/10.1007/s10474-016-0652-8
Key words and phrases
- Jacobi expansion
- Jacobi operator
- symmetrization
- Poisson semigroup
- maximal operator
- Riesz transform
- square function
- spectral multiplier
- Calderón—Zygmund operator