Singular integrals in nonhomogeneous spaces: \(L^2\) and \(L^p\) continuity from Hölder estimates

DOI10.4171/RMI/604zbMath1205.42011MaRDI QIDQ971972

Marco Bramanti

Publication date: 17 May 2010

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1266330127

zbMATH Keywords

singular integralsHölder spaces\(L^p\) spacesnonhomogeneous spaces

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Linear operators on function spaces (general) (47B38)

Related Items (11)

\(L^p\) estimates for degenerate non-local Kolmogorov operators ⋮ Global \(L^{p}\) estimates for degenerate Ornstein-Uhlenbeck operators ⋮ Interior \(W^{1,p}\) regularity and Hölder continuity of weak solutions to a class of divergence Kolmogorov equations with discontinuous coefficients ⋮ Discrete Hölder estimates for a parametrix variation ⋮ On left-invariant Hörmander operators in \(\mathbb R^N\). Applications to Kolmogorov-Fokker-Planck equations ⋮ Non-homogeneous \(Tb\) theorem and random dyadic cubes on metric measure spaces ⋮ Local real analysis in locally homogeneous spaces ⋮ Martingale problems for some degenerate Kolmogorov equations ⋮ An explicit expression for singular integral operators with non-necessarily doubling measures ⋮ Boundary value problems for non-linear first order systems of partial differential equations in higher dimensions, especially in three dimensions ⋮ The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE

Cites Work

• Global \(L^{p}\) estimates for degenerate Ornstein-Uhlenbeck operators
• Schauder estimates for parabolic nondivergence operators of Hörmander type
• Boundedness on inhomogeneous Lipschitz spaces of fractional integrals singular integrals and hypersingular integrals associated to non-doubling measures
• A boundedness criterion for generalized Calderón-Zygmund operators
• Balls and metrics defined by vector fields. I: Basic properties
• Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation. (Calderón-Zygmund operators, para-accretive functions and interpolation)
• Lipschitz functions on spaces of homogeneous type
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• On the boundedness of singular integrals
• The \(Tb\)-theorem on non-homogeneous spaces.
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Intertwining operators for semisimple groups
• Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs
• Singular Integral Operators and Differential Equations
• Application of a Theorem of M. G. Krein to Singular Integrals
• Cotlar's inequality without the doubling condition and existence of principal values for the Cauchy integral of measures
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• A proof of the weak \((1,1)\) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition
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