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arXiv · 2608.23958

BMO Classification for Two-Dimensional Dunkl Newton and Green Kernels

Ji Li·Lixin Yan·Huohao Zhang
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Abstract

Using Gaussian heat-kernel estimates, we classify planar Dunkl Newton kernels in weighted Euclidean BMO and obtain the corresponding local classification for unit-ball Green kernels. For atomic Newton potentials supported on a regular reflection orbit, orbit BMO detects exactly whether the coefficients are constant along the orbit. We also prove an intrinsic Dunkl--CLMS theorem in the heat-semigroup Hardy space and derive intrinsic and Euclidean-source Newton--Wente estimates, extending the BMO--Hardy-space method of Chanillo and Li to the Dunkl setting. Further consequences include sharp local atomic estimates, same-domain criteria, a localized $L^1$-to-BMO bound, and a Brezis--Merle-type estimate.

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Ji Li, Lixin Yan, Huohao Zhang. 2026-08-25. BMO Classification for Two-Dimensional Dunkl Newton and Green Kernels. https://arxiv.org/abs/2608.23958

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