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Matematicheskie Zametki, 2018, Volume 103, Issue 4, Pages 544–548
DOI: https://doi.org/10.4213/mzm11565 (Mi mzm11565) 		 
Remarks on Weak-Type Estimates for Certain Grand Square Functions

Yi Huangabc

a Université Paris-Sud, France
b Université Paris-Saclay, France
c Nanjing Normal University, China
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DOI: https://doi.org/10.4213/mzm11565
Abstract: In this note we extend weak-type estimates obtained recently by A. K. Lerner to certain grand square functions by using a simple argument in terms of real variables. In this way, we improve a weak-type $L^1$-estimate for grand Littlewood–Paley operators due to N. N. Osipov.
Keywords: Littlewood–Paley operators, (grand) square functions, sharp aperture dependence, weak-type estimates, Lorentz spaces.
Funding agency Grant number
Agence Nationale de la Recherche ANR-12-BS01-0013-01
This work was supported in part by the ANR project “Harmonic Analysis at Its Boundaries” under grant no. ANR-12-BS01-0013-01.
Received: 22.02.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 4, Pages 589–592
DOI: https://doi.org/10.1134/S0001434618030252
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Yi Huang, “Remarks on Weak-Type Estimates for Certain Grand Square Functions”, Mat. Zametki, 103:4 (2018), 544–548; Math. Notes, 103:4 (2018), 589–592
Citation in format AMSBIB
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