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Singular integral operators between the classical type and the product type. (Chinese. English summary) Zbl 1274.42035

Summary: A class of singular integral operators is introduced which can be seen as the middle class between the classical single-parameter singular integral operators and the multi-parameter product singular integral operators. The \(L^p\) (\(p>1\)) boundedness for these operators is obtained, where the \(L^2\) boundedness of these operators is obtained by the method of Fourier transform and integration by part and the \(L^p\) (\(p>1\)) boundedness is obtained by the classical method of Littlewood-Paley-Stein theory.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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