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Weighted multi-parameter mixed Hardy spaces and their applications
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 709-734
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Applying discrete Calderón's identity, we study weighted multi-parameter mixed Hardy space $H^{p}_{\rm mix}(\omega ,\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$. Different from classical multi-parameter Hardy space, this space has characteristics of local Hardy space and Hardy space in different directions, respectively. As applications, we discuss the boundedness on $H^{p}_{\rm mix}(\omega ,\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$ of operators in mixed Journé's class.
Applying discrete Calderón's identity, we study weighted multi-parameter mixed Hardy space $H^{p}_{\rm mix}(\omega ,\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$. Different from classical multi-parameter Hardy space, this space has characteristics of local Hardy space and Hardy space in different directions, respectively. As applications, we discuss the boundedness on $H^{p}_{\rm mix}(\omega ,\mathbb {R}^{n_{1}}\times \mathbb {R}^{n_{2}})$ of operators in mixed Journé's class.
DOI : 10.21136/CMJ.2022.0115-21
Classification : 42B20, 42B25, 42B30, 42B35
Keywords: weight; multi-parameter; mixed Hardy spaces; singular integral operator 
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Ding, Wei; Xu, Yun; Zhu, Yueping. Weighted multi-parameter mixed Hardy spaces and their applications. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 709-734. doi: 10.21136/CMJ.2022.0115-21

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