Bilinear square functions and vector-valued Calderón-Zygmund operators
type: Item
instance of: scholarly article
title: Bilinear square functions and vector-valued Calderón-Zygmund operators
zbMATH Open document ID: 1268.42036
author: Jarod Hart
published in: The Journal of Fourier Analysis and Applications
publication date: 2013-01-29T00:00:00Z
review text: The bilinear square function corresponding to a sequence of kernels \(\theta_{k}:\mathbb{R}^{n}\times\mathbb{R}^{n}\times\mathbb{R}^{n}\rightarrow \mathbb{C}\) is defined by \[ \Bigg(\sum_{k\in\mathbb{Z}}\mid\Theta_{k}(f,g)\mid^{2}\Bigg)^{1/2}, \] where \[ \Theta_{k}(f,g)=\int\int\theta_{k}(x,y,z)f(y)g(z)dydz. \] Optimal conditions on the kernels \(\theta_{k}\) are found to provide boundedness of bilinear square functions on products of Lebesgue, Sobolev and some other spaces of smooth functions. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain boundedness result in the case of products of Lebesgue spaces for the full range of exponents: \(1<p,q<\infty\) and \(1/2<r<\infty\).
reviewed by: Giorgi Oniani
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 6132226
zbMATH Keywords: square function
zbMATH Keywords: Littlewood-Paley
zbMATH Keywords: bilinear
zbMATH Keywords: Calderón-Zygmund operators
MaRDI profile type: Publication
full work available at URL: s00041-012-9238-1
OpenAlex ID: W2005279741
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DOI: 10.1007/S00041-012-9238-1
description: scientific article; zbMATH DE number 6132226