A remark to the \(L^2\) boundedness of parametric Marcinkiewicz integral

DOI10.1016/j.jmaa.2011.09.020zbMath1234.42007OpenAlexW2083357307MaRDI QIDQ655472

Kôzô Yabuta, Qing Ying Xue, Ding, Yong

Publication date: 4 January 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.09.020

zbMATH Keywords

parametric Marcinkiewicz integralHardy space \(H^1(S^{n-1})\)

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20)

Related Items (16)

\(L^p\) bounds for Marcinkiewicz integrals associated to homogeneous mappings ⋮ Fractional type Marcinkiewicz integral operator associated with \(\Theta\)-type generalized fractional kernel and its commutator on non-homogeneous spaces ⋮ Marcinkiewicz type operators with kernels involving Bessel functions ⋮ Integral operators of Marcinkiewicz type on Triebel-Lizorkin spaces ⋮ Boundedness of commutators of Marcinkiewicz integrals on nonhomogeneous metric measure spaces ⋮ Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces ⋮ On Marcinkiewicz integrals associated to compound mappings with rough kernels ⋮ Weighted complete continuity for the commutator of Marcinkiewicz integral ⋮ Marcinkiewicz integrals with rough kernels in \(H^1(S^{n-1})\) ⋮ Fractional type Marcinkiewicz integral operators associated to surfaces ⋮ On the \(L^2\) boundedness for the multiple Littlewood-Paley functions with rough kernels ⋮ A note on Marcinkiewicz integrals along submanifolds of finite type ⋮ Nonlinear operators in fixed point theory with applications to fractional differential and integral equations ⋮ Quantitative weighted L^p bounds for the Marcinkiewicz integral ⋮ Boundedness of Marcinkiewicz integrals on RBMO spaces over nonhomogeneous metric measure spaces ⋮ The boundedness of Marcinkiewicz integrals commutators on non-homogeneous metric measure spaces

Cites Work

• On the \(L^{2}\) boundedness of parametric Marcinkiewicz integral operator
• Estimates for translation invariant operators in \(L^p\) spaces
• CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS
• On the Functions of Littlewood-Paley, Lusin, and Marcinkiewicz
• On the p-independence boundedness property of Calderón-Zygmund theory
• Classical Fourier Analysis
• A problem on rough parametric Marcinkiewicz functions
• On the function of Marcinkiewicz
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