App Store was trademarked in 1998 and later abandonned if that is what you want :
Word Mark APPSTORE
Goods and Services (ABANDONED) IC 042. US 100 101. G & S: providing computer software application hosting services by means of a global computer information network, where such services allow multiple users to rent software applications developed by applicant or third parties
Mark Drawing Code (1) TYPED DRAWING
Serial Number 75542841
Filing Date August 26, 1998
Current Filing Basis 1B
Original Filing Basis 1B
Published for Opposition February 29, 2000
Owner (APPLICANT) SAGE NETWORKS, INC. CORPORATION BY ASSIGNMENT DELAWARE 215 FIRST STREET CAMBRIDGE MASSACHUSETTS 02142