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arXiv · 2503.23592

Multilinear operators on Hardy spaces associated with ball quasi-Banach function spaces

Jian Tan
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Abstract

This paper establishes that multilinear Calder\'on--Zygmund operators and their maximal operators are bounded on Hardy spaces associated with ball quasi-Banach function spaces. Moreover, we also obtain the boundedness of multilinear pseudo-differential operators on local Hardy spaces associated with ball quasi-Banach function spaces. Since these (local) Hardy type spaces encompass a wide range of classical (local) Hardy-type spaces including weighted (local) Hardy spaces, variable (local) Hardy space, (local) Hardy--Morrey space, mixed-norm (local) Hardy space, (local) Hardy--Lorentz space and (local) Hardy--Orlicz spaces, the results presented in this paper are highly general and essentially improve the existing results.

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Jian Tan. 2025-03-30. Multilinear operators on Hardy spaces associated with ball quasi-Banach function spaces. https://arxiv.org/abs/2503.23592

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