For one-dimensional bilinear rough singular integrals, bounded variation of the angular multiplier is equivalent to the antipodal even part of the kernel lying in H¹, which yields the optimal LlogL endpoint and a critical directional endpoint.
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Endpoint Criteria for One-Dimensional Bilinear Rough Singular Integrals
For one-dimensional bilinear rough singular integrals, bounded variation of the angular multiplier is equivalent to the antipodal even part of the kernel lying in H¹, which yields the optimal LlogL endpoint and a critical directional endpoint.