Singular integrals associated with Zygmund dilations on multiparameter weighted Hardy spaces

Key Points

The boundedness of singular integral operators has been established in three-parameter settings, showing significant findings.
Using the Rubio de Francia extrapolation technique, new results are introduced in product Hardy spaces linked to quasi-Banach spaces.
Application to specific function spaces like Herz spaces resulted in entirely new insights, highlighting versatility.
The findings have implications for broader mathematical theories and practices involving function spaces and integral operators.

Abstract

Abstract The aim of this paper is to establish the boundedness of multiparameter singular integral operators associated with Zygmund dilations on product weighted Hardy spaces in the three‐parameter setting. Additionally, we show that this class of operators are bounded on product Hardy spaces associated with ball quasi‐Banach function spaces by employing the Rubio de Francia extrapolation technique. The generality of our result is illustrated by their applicability to concrete function spaces such as product Herz spaces and weighted product Morrey spaces. Even in these specific cases, the application yields entirely new results.

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