Two problems of Calderón-Zygmund theory on product-spaces
type: Item
instance of: scholarly article
title: Two problems of Calderón-Zygmund theory on product-spaces
zbMATH Open document ID: 0638.47026
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74785
review text: R. Fefferman has shown that, on a product-space with two factors, an operator T bounded on \(L^ 2\) maps \(L^{\infty}\) into BMO of the product if the mean oscillation on a rectangle R of the image of a bounded function supported out of a multiple R' of R, is dominated by \(C| R| ^ s| R| ^{-s}\), for some \(s>0\). We show that this result does not extend in general to the case where E has three or more factors but remains true in this case if in addition T is a convolution operator, provided \(s>s_ 0(E)\). We also show that the Calderon-Coifman bicommutators, obtained from the Calderon commutators by multilinear tensor product, are bounded on \(L^ 2\) with norms growing polynomially.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4040629
zbMATH Keywords: mean oscillation
zbMATH Keywords: convolution operator
zbMATH Keywords: Calderon-Coifman bicommutators
zbMATH Keywords: multilinear tensor product
author: Jean-Lin Journé
MaRDI profile type: Publication
OpenAlex ID: W2030863889
cites work: Calderón-Zygmund theory for product domains: H p spaces
cites work: Journé's covering lemma and its extension to higher dimensions
cites work: Calderón-Zygmund operators on product spaces
cites work: Harmonic analysis on product spaces
cites work: Bounded mean oscillation on the polydisk
cites work: A continuous version of duality of \(H^ 1\) with BMO on the bidisc
cites work: A Littlewood-Paley inequality for arbitrary intervals
cites work: Polynomial growth estimates for multilinear singular integral operators
cites work: Carleson measure on the bi-disc
cites work: Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon
cites work: The Calderon-Zygmund Decomposition on Product Domains
DOI: 10.5802/AIF.1125
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4040629