this was Austria-Hungary until 1919! many crownlands.http://www.brainworker.ch/Oesterreich/Austria-hungary.png
present Austria is very small. there can have been possible also a Baumgarten in one of the crownlands, which has now as example a czech name or so. but in present Austria there also is a "Baumgarten an der March" in state Lower-Austria north of Vienna near the slovakian border. present Slovakia was in ols timeas also Austria-Hungary. i thought you mean the Baumgarten belonging to 14th district of Vienna/Wien, as you have posted on Vienna-board.
maybe you ask at the parish-church of Baumgarten am Marchfeld:http://www.erzdioezese-wien.at/edw/organisation/vikariate/de...
no e-mail-adress, so ask at the other e-mail-adress above.http://de.wikipedia.org/wiki/Baumgarten_an_der_Marchhttp://en.wikipedia.org/wiki/Baumgarten_an_der_March
if they find nothing tell me and i will look if there was another Baumgarten in another crownland.
also there is some online, but Baumgarten am Marchfeld is not in list at moment: http://www.matricula-online.eu/?lang=enhttp://maps.google.at/maps?hl=de&q=Baumgarten+an+der+Mar...
to the lastname i think both is possible > Valli, as Vienna has one at gravesearch and also Walli which are to find many more.