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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 $\bbfR\sp n$. Consider the operator $T$ defined by $$Tf(x)=\text{p.v. }\int\sb \bbfR\sp ne\sp{iP(x-y)}K(x-y)f(y)dy.$$ In the paper under review the authors proved the boundedness of $T$ in the Hardy space $H\sp 1$, as well as in some weighted Hardy spaces. [See also the following review].

42B20Singular and oscillatory integrals, several variables
42B30$H^p$-spaces (Fourier analysis)
Full Text: DOI
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