Design of control resource sets (CORESETs) is disclosed for new radio (NR) unlicensed (NR-U) operations with subband access. A default CORESET may be defined for multiple or all subbands within the allocated NR system bandwidth where each subband is covered by a sub-CORESET. When a decoding candidate of the set of decoding candidates spans the boundary of multiple sub-CORESETs, a base station may either remove the overlapping decoding candidate from the set of decoding candidates, shift the decoding candidate into the next location fully within a sub-CORESET, or continue transmission of the decoding candidate while puncturing the portion on the inaccessible subband. In the puncturing option, a user equipment (UE) would perform additional blind decoding in each subband according to the associated sub-CORESET. In additional aspects, after beginning of a transmission opportunity, the UE uses the knowledge of accessible subbands for fast CORESET switching via broadcast or UE-specific signaling.