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Inequalities for strongly singular convolution operators   总被引:12,自引:0,他引:12  
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A note on spherical summation multipliers   总被引:12,自引:0,他引:12  
We give a new proof of a theorem of L. Carleson and P. Sj?lin onL p -boundedness of spherical summation operators in two variables.  相似文献
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We study the rate of growth of sharp fronts of the Quasi-geostrophic equation and 2D incompressible Euler equations. The development of sharp fronts are due to a mechanism that piles up level sets very fast. Under a semi-uniform collapse, we obtain a lower bound on the minimum distance between the level sets.

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Harmonic functions are studied on complete Riemannian manifolds. A decay estimate is given for bounded harmonic functions of variable sign. For unbounded harmonic functions of variable sign, relations are derived between growth properties and nodal domains. On Riemannian manifolds of nonnegative Ricci curvature, it has been conjectured that harmonic functions, having at most a given order of polynomial growth, must form a finite dimensional vector space. This conjecture is established in certain special cases.  相似文献
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SharpL p boundedness results are proven for pseudo-differential operators in the classS m .  相似文献
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In this paper we prove finiteness principles for \({C^m{({\mathbb{R}^n},{\mathbb{R}^D)}}}\) and \({C^{m-1,1}(\mathbb{R}^n,\mathbb{R}^D)}\) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is \({X=\mathbb{R}^n}\).  相似文献
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