Vlad, the only way I know to go about this is to use two parameters - to define the start and end date of your period, and then do the filtering based on these in a per-connection basis. This is because 1) the filters are not considered part of the view, hence no blending will occur on fields that you filter on, and 2) parameters are global for the workbook. The drawback is that you effectively have static parameters that do not pick up the data available in your database, hence the user may select inappropriate values.
See the attached mockup based off the standard Tableau datasets for more info.
347731.twbx 1.1 MB