Multi-parameter extensions of a theorem of Pichorides
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- by Odysseas Bakas, Salvador Rodríguez-López and Alan A. Sola
- Proc. Amer. Math. Soc. 147 (2019), 1081-1095
- DOI: https://doi.org/10.1090/proc/14251
- Published electronically: November 16, 2018
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Abstract:
Extending work of Pichorides and Zygmund to the $d$-dimensional setting, we show that the supremum of $L^p$-norms of the Littlewood–Paley square function over the unit ball of the analytic Hardy spaces $H^p_A(\mathbb {T}^d)$ blows up like $(p-1)^{-d}$ as $p\to 1^+$. Furthermore, we obtain an $L\log ^d L$-estimate for square functions on $H^1_A(\mathbb {T}^d)$. Euclidean variants of Pichorides’ theorem are also obtained.References
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Bibliographic Information
- Odysseas Bakas
- Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
- Email: bakas@math.su.se
- Salvador Rodríguez-López
- Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
- Email: s.rodriguez-lopez@math.su.se
- Alan A. Sola
- Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
- MR Author ID: 804661
- Email: sola@math.su.se
- Received by editor(s): February 5, 2018
- Received by editor(s) in revised form: February 22, 2018, and May 29, 2018
- Published electronically: November 16, 2018
- Additional Notes: The second author was partially supported by the Spanish Government grant MTM2016-75196-P
- Communicated by: Stephan Ramon Garcia
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1081-1095
- MSC (2010): Primary 42B15, 42B25, 42B30
- DOI: https://doi.org/10.1090/proc/14251
- MathSciNet review: 3896058