I think your Select - Select in field action with above search string should also work in Ajax client.
Have you double checked that the expression produces a search string that seems to be ok (i.e. both date limits and valid date format compared to Datum field)?
You can also create a button to test your action in the Ajax client.
I assume (if you checked the expression), that it's not a matter of your search expression, but of the trigger you are using. What trigger does call the action? Not all triggers work in Ajax, AFAIR.
Master G is right
My Expression works perfectly in the desktop version. Than I put it on the server and trigger(onsheetactivate) does not work. :-( ...
Later I searched the forums for the triggers, and found some disappointing discussions. Reload and On Open trigger seem to work properly.
I could live with that, when I can manage to set a clear state, which is same like the onload. Else the user gets all weeks shown which are in system. I tried a bookmark, but I couldn't get it to work, that the bookmark is updated for the actual date. Best way would be to shrink data, but it's no sensitive data, so it is no problem if the user has the possibility to explore the data.
@Gysbert: I don't use any buttons, in fact there is only one sheet at the moment, because of the problem described here.