Lp-estimates for the wave equation on the Heisenberg group.

Detlef Müller; Elias M. Stein

Displaying similar documents to “Lp-estimates for the wave equation on the Heisenberg group.”

Dispersive Estimates of Solutions to the Wave Equation with a Potential in Dimensions Two and Three

Cardoso, Fernando, Cuevas, Claudio, Vodev, Georgi (2005)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35L15, 35B40, 47F05. We prove dispersive estimates for solutions to the wave equation with a real-valued potential V.

Ferromagnetic integrals, correlations and maximum principles

Johannes Sjöstrand (1994)

Annales de l'institut Fourier

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For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.

Fatou and Korányi-Vági type theorems on the minimal ball.

Nguyên Viêt Anh (2002)

Publicacions Matemàtiques

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In this paper we develop the H(p ≥ 1) theory on the minimal ball. After identifying the admissible approach regions, we establish theorems of Fatou and Koráanyi-Vági type on this ball.

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let $R (λ)$ be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that $\int_{1}^{T} {| R (t) |}^{2} d t = c T^{\frac{5}{2}} + O_{δ} (T^{\frac{9}{4} + δ})$ , where $c$ is a specific nonzero constant and $δ$ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that $R (t) = O_{δ} (t^{\frac{3}{4} + δ})$ .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the $2 n + 1$ -dimensional case. ...

On the Hölder continuity of solutions of second order elliptic equations in two variables

L. C. Piccinini, S. Spagnolo (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.

Cédric Villani (1999)

Revista Matemática Iberoamericana

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We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L(R) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.

The existence and the continuation of holomorphic solutions for convolution equations in tube domains

Ryuichi Ishimura, Yasunori Okada (1994)

Bulletin de la Société Mathématique de France

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