Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

Steve Hofmann; Marius Mitrea; Sylvie Monniaux

Displaying similar documents to “Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds”

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of $d$ –actions (and the corresponding $d$ -dimensional Lie algebras) defined by commuting singular vector fields in $ℂ^{n}$ fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of $d$ vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables

Miroslav Zelený (2008)

Annales de l’institut Fourier

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We construct a differentiable function $f : R^{n} \to R$ ( $n \geq 2$ ) such that the set ${(\nabla f)}^{- 1} (B (0, 1))$ is a nonempty set of Hausdorff dimension $1$ . This answers a question posed by Z. Buczolich.

Semi-classical functional calculus on manifolds with ends and weighted $L^{p}$ estimates

Jean-Marc Bouclet (2011)

Annales de l’institut Fourier

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For a class of non compact Riemannian manifolds with ends, we give semi-classical expansions of bounded functions of the Laplacian. We then study related $L^{p}$ boundedness properties of these operators and show in particular that, although they are not bounded on $L^{p}$ in general, they are always bounded on suitable weighted $L^{p}$ spaces.

Maximal inequalities and Riesz transform estimates on $L^{p}$ spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher, Besma Ben Ali (2007)

Annales de l’institut Fourier

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We show various $L^{p}$ estimates for Schrödinger operators $- Δ + V$ on $ℝ^{n}$ and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of $- Δ + V$ and their gradients.

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

Guliyev, Vagif, Hasanov, Javanshir (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 42B20, 42B25, 42B35 We consider the generalized shift operator, generated by the Laplace- Bessel differential operator [...] The Bn -maximal functions and the Bn - Riesz potentials, generated by the Laplace-Bessel differential operator ∆Bn are investigated. We study the Bn - Riesz potentials in the Bn - Morrey spaces and Bn - BMO spaces. An inequality of Sobolev - Morrey type is established for the Bn - Riesz potentials. ...

Displaying similar documents to “Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds”

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables

Semi-classical functional calculus on manifolds with ends and weighted L p estimates

Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

Semi-classical functional calculus on manifolds with ends and weighted $L^{p}$ estimates

Maximal inequalities and Riesz transform estimates on $L^{p}$ spaces for Schrödinger operators with nonnegative potentials