Estimations of Hölder Regularities and Direction o

Authors: Jouni Sampo Songkiat Sumetkijakan

Publish Date: 2008/11/19

Volume: 15, Issue: 1, Pages: 58-79

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Abstract

Using Hart Smith’s and curvelet transforms new necessary and new sufficient conditions for an L 2ℝ2 function to possess Hölder regularity uniform and pointwise with exponent α0 are given Similar to the characterization of Hölder regularity by the continuous wavelet transform the conditions here are in terms of bounds of the transforms across fine scales However due to the parabolic scaling the sufficient and necessary conditions differ in both the uniform and pointwise cases We also investigate squareintegrable functions with sufficiently smooth background Specifically sufficient and necessary conditions which include the special case with 1dimensional singularity line are derived for pointwise Hölder exponent Inside their “cones” of influence these conditions are practically the same giving nearcharacterization of direction of singularity

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