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Boundedness of oscillatory singular integrals on Hardy spaces. (English) Zbl 0779.42007

Let \(K\) be a Calderón-Zygmund kernel and \(P\) a polynomial in \(\mathbb{R}^ n\). Consider the operator \(T\) defined by \[ Tf(x)=\text{p.v. }\int_ \mathbb{R}^ ne^{iP(x-y)}K(x-y)f(y)dy. \] In the paper under review the authors proved the boundedness of \(T\) in the Hardy space \(H^ 1\), as well as in some weighted Hardy spaces. [See also the following review].
Reviewer: N.Jacob (Erlangen)

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B30 \(H^p\)-spaces

Citations:

Zbl 0779.42008
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References:

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