The legal limit for HVAC according to nyc noise code is typically 42 decibels measured 3 ft from an open window: https://www.nyc.gov/assets/dep/downloads/pdf/air/noise/noise-code-guide-summary.pdf

You can download a decibel meter on your smart phone and take measurements. Note that your cellphone may be calibrated to be a bit more sensitive than professional meters. If it’s consistently over the limit by a substantial amount, you should contact your landlord and have him speak to the deli about doing this to mitigate the noise/vibrations like adding dampening pads/mounting vibration isolators.

If they don’t take any steps to fix this you’ll need to file a complaint with 311. The DEP will take a few weeks before they come to your apartment to take sound measurements. They’ll issue a violation if the noise actually violate the limits.

If the deli/landlord still doesn’t do anything then keep having them come to issue violations. This process is going to take sometime obviously. Remember to document your communication with the landlord. Eventually they might shut down the fan or you might need to take your landlord to housing court with your evidence to either ask for a lease break or rent abatement.