A Littlewood-Paley inequality for the Carleson operator.

DOI10.1007/BF02511540zbMath1049.42010MaRDI QIDQ1588369

Elena Prestini, Per Sjoelin

Publication date: 2000

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

Full work available at URL: https://eudml.org/doc/59654

zbMATH Keywords

singular integralFourier seriesLittlewood-Paley inequality\(L^p\) estimatesmaximal singular operatormaximal partial sum operator

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (11)

Vector valued maximal Carleson type operators on the weighted Lorentz spaces ⋮ Weighted \(L^p\)-bounds for the Carleson type maximal operator with kernel satisfying mild regularity ⋮ Singular integrals with bilinear phases ⋮ Almost orthogonal operators on the bitorus. II ⋮ Estimates for Hilbert transforms along variable general curves ⋮ Hilbert transforms along double variable fractional monomials ⋮ A Wiener-Wintner theorem for the Hilbert transform ⋮ \(L^p\) boundedness of Carleson type maximal operators with nonsmooth kernels ⋮ Maximal polynomial modulations of singular integrals ⋮ \(L^p\) boundedness of Carleson \& Hilbert transforms along plane curves with certain curvature constraints ⋮ Weighted $L^{p}$ boundedness of Carleson type maximal operators

Cites Work

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• Calderón-Zygmund theory for operator-valued kernels
• On convergence and growth of partial sums of Fourier series
• Convergence almost everywhere of certain singular integrals and multiple Fourier series
• Singular Integrals on Product Spaces Related to the Carleson Operator
• Pointwise convergence of Fourier series

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