Should I include proofs for known theorems in a doctoral thesis in mathematics? In general, in a thesis we recall the theorems of other mathematicians before stating our results published in a scientific journal. My question, is it essential to give the proofs of these theorems (for example these theorems are mentioned in the first chapter  of the thesis) or I will give the outline of the demonstration or only the statements ?
This is something you should discuss with your adviser. It really should depend on the theorems; how important is including their proofs to the understanding of what one has done? Also, how long are their proofs? And how much is your own work using proofs which build off of those theorems? There's no simply response here. You'll see both dissertations and papers where relevant theorems have their proofs included, and others where they are referenced.