2 problems

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Non-membership of the Born-Jordan kernel in $M^{1,\infty}$
Orlik's conjecture. The Born-Jordan kernel does not belong to the modulation space $M^{1,\infty}(\mathbb{R}^{2d})$ :
Conjectureopenborn-jordan-quantization modulation-spacesarXiv posted 2 days ago
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Optimal boundedness condition for Born-Jordan pseudodifferential operators
Optimal boundedness conjecture. The condition
Conjectureopenborn-jordan-quantization modulation-spaces pseudodifferential-operatorsarXiv posted 2 days ago

Non-membership of the Born-Jordan kernel in M1,∞M^{1,\infty}M1,∞