Yes, air purifiers or ionizers do work but only if you get a quality one. The ones your going to buy at Walmart for $20 will most likely have no impact whatsoever. I have a quality one I bought at Sharper Image that does a good job, it resolved my allergy problems to a large extent. You may also want to look at buying an activated carbon air scrubber. You can find instructions on how to build one yourself online or you can buy them off ebay, or other websites.
