具有非齐次核的抛物型奇异积分
Parabolic Singular Integrals with Nonhomogeneous Kernels
AI总结：
本文在正则 Lip(1,1/2) 抛物图上证明了具有非齐次核的“良好”抛物型奇异积分的 $L^2$ 有界性，将已有齐次核结果推广到与抛物型一致可整流性相关的非齐次情形，并融合了 Christ 讲义方法与 Coifman-David-Meyer 技巧。
摘要：
我们建立了所有“良好”抛物型奇异积分在“良好抛物图”（即正则 Lip(1,1/2) 图）上的 $L^2$ 有界性。本文的新颖之处在于我们包含了非齐次核，这与抛物型一致可整流性理论相关。此前，第三作者已处理过齐次核的情形。本证明结合了该工作的方法（该方法又基于 Christ 的 CBMS 讲义中所述方法）与 Coifman-David-Meyer 的技巧。
英文摘要：
We establish $L^2$ boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here is that we include non-homogeneous kernels, which are relevant to the theory of parabolic uniform rectifiability. Previously, the third named author had treated the case of homogeneous kernels. The present proof combines the methods of that work (which in turn was based on methods described in Christ's CBMS lecture notes), with the techniques of Coifman-David-Meyer.
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