Capture flag and entangled invariance beyond multiplier operators

Determine how the invariance of specialized multi-parameter singular integrals should be captured at the singular-integral level for non-convolution operators, particularly outside the class of Fourier multipliers.

Background

The paper emphasizes that flag and Zygmund singular integrals possess additional entanglement, decay, and geometric invariance that are not present in generic multi-parameter operators. Although the paper develops a natural non-convolution flag framework, it states that the appropriate way to encode these invariances at the singular-integral level is not generally understood, especially beyond multiplier examples.