When I was checking in online with Delta airlines, it was mentioned that household cleaners are restricted by TSA. What is TSA's definition of household cleaners?
Many household cleaners are liquids, so they'd be restricted by the 3-1-1 liquids rule for carry-on luggage. Beyond that, TSA rules and FAA hazardous material rules would prohibit a number of common cleaning chemicals in carry-on or checked bags: bleach, flammable liquids, flammable aerosols (and non-toiletry non-flammable aerosols in carry-on bags), etc... Some are permitted, such as detergent and soap, as are ordinary cleaning tools like sponges and rags. In many cases, household cleaners can be easily purchased at your destination instead of bringing them with you, which is a safer choice unless you're sure what is in your products and that it is nonhazardous.
You can check specific items by searching both the TSA's website and the FAA's PackSafe tool. You can also contact the TSA on Facebook or Twitter with questions.