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Two problems of Calderón-Zygmund theory on product-spaces

Jean-Lin Journé — 1988

Annales de l'institut Fourier

R. Fefferman has shown that, on a product-space with two factors, an operator T bounded on L 2 maps L 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,...

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