منابع مشابه
SHARP LIPSCHITZ ESTIMATES FOR OPERATOR ∂̄M ON A q-CONCAVE CR MANIFOLD
We prove that the integral operators Rr and Hr constructed in [P] and such that f = ∂̄MRr(f) + Rr+1(∂̄Mf) +Hr(f), for a differential form f ∈ C (0,r) (M) on a regular q-concave CR manifold M admit sharp estimates in the Lipschitz scale.
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We construct integral operators Rr and Hr on a regular q-pseudoconcave CR manifold M such that f = ∂̄MRr(f) + Rr+1(∂̄Mf) +Hr(f), for f ∈ C (0,r) (M) and prove sharp estimates in a special Lipschitz scale.
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We prove sharp Morawetz estimates – global in time with a singular weight in the spatial variables – for the linear wave, Klein–Gordon and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.
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We establish Lp bounds on L2 normalized spectral clusters for selfadjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all 2 ≤ p ≤ ∞, up to logarithmic losses for 6 < p ≤ 8. In higher dimensions we obtain best possible bounds for a limited range of p.
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Orthogonal polynomials have been used to produce sharp estimates in Harmonic Analysis in several instances. The first most notorious and original use was in Beckner’s thesis [1], where he proved the sharp Hausdorff-Young inequality using Hermite polynomial expansions. More recently, Foschi [4] used spherical harmonics and Gegenbauer polynomials in his proof of the sharp Tomas-Stein adjoint Four...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-06-08569-8