Two problems of Calderón-Zygmund theory on product-spaces

@article{Journé1988,
abstract = {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 $C\vert R\vert ^ s\vert R\vert ^\{-s\}$, 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.},
author = {Journé, Jean-Lin},
journal = {Annales de l'institut Fourier},
keywords = {mean oscillation; convolution operator; Calderon-Coifman bicommutators; multilinear tensor product},
language = {eng},
number = {1},
pages = {111-132},
publisher = {Association des Annales de l'Institut Fourier},
title = {Two problems of Calderón-Zygmund theory on product-spaces},
url = {http://eudml.org/doc/74785},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Journé, Jean-Lin
TI - Two problems of Calderón-Zygmund theory on product-spaces
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 1
SP - 111
EP - 132
AB - 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 $C\vert R\vert ^ s\vert R\vert ^{-s}$, 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.
LA - eng
KW - mean oscillation; convolution operator; Calderon-Coifman bicommutators; multilinear tensor product
UR - http://eudml.org/doc/74785
ER -