A 110V air purifier comes with a 100-240V adapter
If the device has a 100-240V adapter, it's a 100-240V device, not a 110V device. Or more likely it's a (some lower DC voltage you have not looked at - should be printed on the adapter, usually in tiny faint type) device with an adapter that is 100-240V

So, you should not need anything more than a way to plug its adapter in to use with 240VAC