Displaying similar documents to “Why the Riesz transforms are averages of the dyadic shifts?”

The generalizations of integral analog of the Leibniz rule on the G-convolutions.

Semyon B. Yakubovich, Yurii F. Luchko (1991)

Extracta Mathematicae

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An integral analog of the Leibniz rule for the operators of fractional calculus was considered in paper [1]. These operators are known to belong to the class of convolution transforms [2]. It seems very natural to try to obtain some new integral analog of the Leibniz rule for other convolution operators. We have found a general method for constructing such integral analogs on the base of notion of G-convolution [4]. Several results obtained by this method are represented in this article. ...

Two problems of Calderón-Zygmund theory on product-spaces

Jean-Lin Journé (1988)

Annales de l'institut Fourier

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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...

The boundedness of Calderón-Zygmund operators on the spaces F .

Michel Frazier, Rodolfo Torres, Guido Weiss (1988)

Revista Matemática Iberoamericana

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Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the form Tf(x) = límε→0 ∫|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.