Under commercial tenancy law, who is responsible for ensuring the zoning laws are being up held?

Where? This is a very general question.

There is very little law that applies to commercial tenancies. The lease controls the entire situation. Most leases I've seen state that the landlord is responsible for meeting the municipal zoning requirements for the entire structure but that the tenant is responsible for meeting the zoning requirements for their individual business. Read your lease carefully to see what applies in your situation.