We recently reported that there was a wave of account bans going out, and now it looks like Niantic are finally sending out waves of emails to users that have had the accounts banned.
Reddit users are reporting that if you used the same email address for your Pokémon Trainer Club account as your Google Account login then it would be worth trying to login with your Google Account as there is a chance that it hasn’t been banned. Source.
If you have been banned, you can submit a ban appeal here.
In-App Purchases Refund
Users have also been reporting that they have been able to get refunds from both the Google Play store and also the Apple Store even if there account has been permanently banned. If your account has been banned and you would like a refund for any purchases you made, it is worth contacting Google Play and Apple Store support.