Bass, Richard F.Burdzy, Krzysztof2005-10-172005-10-172002-05-21Annales Henri Poincaré 38 (2002): 799-8001424-0667http://hdl.handle.net/1773/2135The original verison appeared in the Annales Henri Poincaré 37 (2001) 627–642.For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all functions whose Hölder norm of order [sigma] is less than or equal to 1. We show that the supremum of L [superscript] f [subscript] 1 over f in S [subscript] [sigma] is finite if [sigma] > 5/6 and infinite if [sigma] < 1/2.176738 bytesapplication/pdfen-USBrownian motionHölder normArticle