Unfortunately, there's no easy way to view the total logged time per user directly in Jira. There's the time tracking reporting available (Reports -> Time Tracking Report), but it only shows the total time logged per Jira issue, which includes the time that everyone has logged into the particular issue.
One way to easily see all of your (or other users') worklogs is via third-party apps. There's a cheap solution that we have built at SolDevelo, that allows to easily check the worklogs of any user during the selected time range. Worklogs - Time Reports for Jira are available for both Jira Server and Jira Cloud. Here's how the report looks like:
there is another possible solution we (END2END) have developed in our marketplace app Worklog express.
There is a quick form you can use to create worklogs on multiple Jira issues defined by JQL. You can also filter users for which you want to display totals in a defined period of time while having an option to create additional or edit existing logs.
There is also a possibility to export all worklog related data to excel and create your own reports. You can find more info on Worklog express documentation.