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.)