A note on Marcinkiewicz integrals along submanifolds of finite type (Q725177)
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scientific article; zbMATH DE number 6912078
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on Marcinkiewicz integrals along submanifolds of finite type |
scientific article; zbMATH DE number 6912078 |
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A note on Marcinkiewicz integrals along submanifolds of finite type (English)
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1 August 2018
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Summary: We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions on the integral kernels, the \(L^p\) bounds will be established for such operators. As applications, the corresponding results for parametric Marcinkiewicz integrals related to area integrals and Littlewood-Paley \(g_\lambda^\ast\) functions are also given.
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rough kernels
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\(L^p\) bounds
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area integrals
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Littlewood-Paley \(g_\lambda^\ast\) functions
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