Once the user has uploaded your PDF (to the browser), they can do something with it. They can save it elsewhere on the hard drive. Even if you somehow disabled this, anyone can intercept network traffic with a third-party application and save the PDF in this way.
It is best to use a digital rights management tool so that the user cannot distribute the PDF file, even if he downloads it. For example, FileOpen or Adobe Content Server. As you can see, such tools can (technically) prevent printing, force expiration, etc.
Please note that this is most useful for users who might accidentally download or distribute data. Malicious users can circumvent these restrictions, for example. Bypassing the printing restrictions by taking a screenshot of each page and printing it.
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