Normally when I think of a log for a user I think of a job log rather than the QHST log. If you are seeking the job logs for a given user then a command such as ‘WRKJOBLOG JOBLOGSTT(*PENDING *SPOOLED) PERIOD((*AVAIL *BEGIN) (*AVAIL *END)) JOB(MY_USER/*ALL)’ would show the list of pending and spooled job logs for the user MY_USER. Is this what you’re looking for?
It tells me that Command WRKJOBLOG in Library *LIBL not found.
WRKJOBLOG is a V5R4 command. You are evidently on an earlier release.