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Sine kernel asymptotics for a class of singular measures
singular measures math
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2010/11/19
We construct a family of measures on $\bbR$ that are purely singular with respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics in the bulk. The measures are best described v...
Convolutions of singular measures and applications to the Zakharov system
Convolution estimates transversal submanifolds L2 bounds
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2010/12/8
Uniform L2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimen-sion. The results of Bennett-Bez are used to extend previous ...
Convolution Operators with Homogeneous Singular Measures on $R^{3}$ of Polynomial Type. The Remainder Case
Convolution operators Singular measures
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2008/7/2
Convolution Operators with Homogeneous Singular Measures on $R^{3}$ of Polynomial Type. The Remainder Case.
SINGULAR MEASURES AND CONVOLUTION OPERATORS
Hardy--Littlewood maximal function Weak type inequalities Singular measures Convolution operators
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2007/12/11
We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type $(1,1)$ inequalities. As an applicat...