On the Lp boundedness of rough parametric Marcinkiewicz functions
On the Lp boundedness of rough parametric Marcinkiewicz functions
Summary: In this paper, we study the \(L^p\) boundedness of a class of parametric Marcinkiewicz integral operators with rough kernels in \( L(\log^{+}L)(\mathbb{S}^{n-1})\). Our result in this paper solves an open problem left by the authors of [J. Aust. Math. Soc. 72, No.~1, 13--21 (2002; Zbl 0993.42008)].
- Qatar University Qatar
Parametric Marcinkiewicz operators, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Rough kernels, rough kernels, parametric maximal functions, Parametric maximal functions, Multipliers for harmonic analysis in several variables, Fourier transforms
Parametric Marcinkiewicz operators, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Rough kernels, rough kernels, parametric maximal functions, Parametric maximal functions, Multipliers for harmonic analysis in several variables, Fourier transforms
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