Pan-frying/sauteeing releases airborne particulate matter (PM) and volatile organic compounds (VOCs), both of which are bad for your acute and long-term health. If cooking fumes aren’t being vented to the great outdoors, then that air needs to be filtered to remove those components. Look for a portable air filtration unit with HEPA filtration for the PM and an activated charcoal filter for the VOCs, and make sure you get at least one that’s appropriately sized for the room in which it’ll be used (in this case, the kitchen).
To keep an eye on indoor air quality (so that you know whether you are adequately filtering), I highly recommend an air quality monitor like Foobot or PurpleAir. The Foobot has an edge over the PurpleAir in that it measures VOCs along with PM. There are plenty of other products out there, but quality varies. To help cut through all the bullshit, the South Coast Air Quality Management District has a program that evaluates consumer-grade air quality monitors and publishes results. Here’s their Air Quality Sensor Performance Evaluation Center; if you’re considering the purchase of a monitor, check their PM/gaseous sensor evaluation page first and see what they think of it.