Multiparameter singular integrals and maximal functions

DOI10.5802/aif.1304zbMath0760.42008OpenAlexW2042353004MaRDI QIDQ1203380

Fulvio Ricci, Elias M. Stein

Publication date: 8 February 1993

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1992__42_3_637_0

zbMATH Keywords

product domainsmaximal operatorshomogeneous manifoldssingular integral operatorsmaximal functionsCalderón-Zygmund kernels

Mathematics Subject Classification ID

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

Related Items (49)

Maximal functions with polynomial densities in lacunary directions ⋮ Unboundedness for some strong maximal functions on weighted Lebesgue spaces ⋮ Zygmund type and flag type maximal functions, and sparse operators ⋮ Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups. I ⋮ Parabolic Marcinkiewicz integrals on product spaces and extrapolation ⋮ Mixed Lipschitz spaces and their applications ⋮ \(L^p\) bounds for Marcinkiewicz integrals associated to homogeneous mappings ⋮ Multi-parameter maximal operators associated with finite measures and arbitrary sets of parameters ⋮ Multi-parameter singular Radon transforms. I: The \(L^2\) theory ⋮ Rough Marcinkiewicz integrals with mixed homogeneity on product spaces ⋮ Sublinear operators on mixed-norm Hardy spaces with variable exponents ⋮ Calderón-Zygmund operators on homogeneous product Lipschitz spaces ⋮ A class of multiparameter oscillatory singular integral operators: endpoint Hardy space bounds ⋮ Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases ⋮ Multiple Hilbert transforms associated with polynomials ⋮ Boundedness of inhomogeneous Journé's type operators on multi-parameter local Hardy spaces ⋮ Atomic decomposition of weighted multi-parameter mixed Hardy spaces ⋮ Duality of three-parameter Hardy spaces associated with a sum of two flag singular integrals ⋮ Three-parameter Hardy spaces associated with a sum of two flag singular integrals ⋮ On singular integrals and maximal operators along surfaces of revolution on product domains ⋮ \(L^{\vec{p}}-L^{\vec{q}}\) boundedness of multiparameter Forelli-Rudin type operators on the product of unit balls of \(\mathbb{C}^n\) ⋮ An oscillatory integral estimate associated to rational phases ⋮ Exotic Calderón-Zygmund operators ⋮ Boundedness of singular integrals on multiparameter weighted Hardy spaces \(H^p_w(\mathbb R^n \times \mathbb R^m)\) ⋮ Maximal operators associated with some singular submanifolds ⋮ Boundedness of multi-parameter pseudo-differential operators on multi-parameter Lipschitz spaces ⋮ DOUBLE HILBERT TRANSFORMS ALONG POLYNOMIAL SURFACES IN R³ ⋮ Rough singular integrals associated to surfaces of revolution ⋮ Mixed radial-angular integrability for rough singular integrals and maximal operators ⋮ Multiparameter singular integrals on the Heisenberg group: uniform estimates ⋮ Double Hilbert transforms along polynomial surfaces in \(\mathbb{R}^3\) ⋮ \(L^p\) estimates for rough singular integrals associated to some hypersurfaces ⋮ Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals ⋮ On rough Marcinkiewicz integrals along surfaces ⋮ Singular integrals with flag kernels and analysis on quadratic CR manifolds ⋮ Adapting product kernels to curves in the plane ⋮ Singular integral operators associated to curves with rational components ⋮ Parabolic maximal operators along surfaces of revolution with rough kernels ⋮ Duality of multi-parameter Triebel-Lizorkin spaces associated with the composition of two singular integral operators ⋮ Anisotropic Fourier multipliers and singular integrals for vector-valued functions ⋮ \(L^p\) boundedness for parabolic Littlewood-Paley operators with rough kernels belonging to block spaces ⋮ Multiparameter singular integrals and maximal operators along flat surfaces ⋮ Triple Hilbert transforms along polynomial surfaces in \(\mathbb{R}^4\) ⋮ Dual spaces of multiparameter local Hardy spaces ⋮ Multi-parameter local Hardy spaces ⋮ Singular integrals associated with Zygmund dilations ⋮ Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces ⋮ A biparameter decomposition of Davis–Garsia type ⋮ Inhomogeneous Lipschitz spaces associated with flag singular integrals and their applications

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