Lusin functions on product spaces
type: Item
instance of: scholarly article
title: Lusin functions on product spaces
zbMATH Open document ID: 0652.42007
author: Shuichi Sato
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: The author extends to the product space setting parts of the Caldéron- Torchinsky theory of parabolic \(H^ p\) spaces. In particular he shows the equivalence of the \(L^ p\) `norms' of the Lusin functions and the nontangential maximal functions arising from certain two-parameter families of linear transformations on product spaces. An extension of the weak type estimate for the double Hilbert transform [cf. \textit{C. Fefferman}, Studia Math. 44, 1-15 (1972; Zbl 0239.44006)] is provided as an application of the theory.
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 4063751
zbMATH Keywords: Caldéron-Torchinsky theory
zbMATH Keywords: parabolic \(H^ p\) spaces
zbMATH Keywords: Lusin functions
zbMATH Keywords: nontangential maximal functions
reviewed by: Mario Milman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4063751