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Endpoint mapping properties of the Littlewood–Paley square function
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 12019 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 157, no 1, p. 1-15Article in journal (Refereed) Published
Abstract [en]

We give an alternative proof of a theorem due to Bourgain concerning the growth of the constant in the Littlewood-Paley inequality on T as p -> 1(+). Our argument is based on the endpoint mapping properties of Marcinkiewicz multiplier operators, obtained by Tao and Wright, and on Tao's converse extrapolation theorem. Our method also establishes the growth of the constant in the Littlewood-Paley inequality on T-n as p -> 1(+). Furthermore, we obtain sharp weak-type inequalities for the Littlewood-Paley square function on T-n, but when n >= 2, the weak-type endpoint estimate on the product Hardy space over the n-torus fails, in contrast to what happens when n = 1.

Place, publisher, year, edition, pages
2019. Vol. 157, no 1, p. 1-15
Keywords [en]
Littlewood-Paley square function, endpoint mapping properties
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-170241DOI: 10.4064/cm7396-4-2018ISI: 000469877600001OAI: oai:DiVA.org:su-170241DiVA, id: diva2:1329419
Available from: 2019-06-24 Created: 2019-06-24 Last updated: 2019-06-24Bibliographically approved

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