\(L^{p} (\mathbb R^{m} \times \mathbb R^{n})\) boundedness for the Marcinkiewicz integral on product spaces

DOI10.1360/03ys9008zbMath1217.42032OpenAlexW1563117438MaRDI QIDQ551739

Lu, Shanzhen, Yan, Dunyan, Guo'en Hu

Publication date: 21 July 2011

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1360/03ys9008

zbMATH Keywords

Littlewood-Paley theoryFourier transform estimatemultiple Marcinkiewicz integral

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Related Items (9)

Rough Marcinkiewicz integrals with mixed homogeneity on product spaces ⋮ Marcinkiewicz integral with rough kernels ⋮ Multiple parametric Marcinkiewicz integrals with mixed homogeneity along surfaces ⋮ Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces ⋮ A rough multiple Marcinkiewicz integral along continuous surfaces ⋮ Rough Marcinkiewicz integrals along certain smooth curves ⋮ On the \(L^2\) boundedness for the multiple Littlewood-Paley functions with rough kernels ⋮ \(L^{p}\) bounds for Marcinkiewicz integrals associated to surfaces of revolution ⋮ The boundedness of Marcinkiewicz integrals commutators on non-homogeneous metric measure spaces

Cites Work

• Unnamed Item
• Multiple singular integrals and maximal functions along hypersurfaces
• \(L^2\)-boundedness of a Marcinkiewicz integral with rough kernel
• On the Functions of Littlewood-Paley, Lusin, and Marcinkiewicz
• L^p bounds for singular integrals and maximal singular integrals with rough kernels

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