Weekly calendar based on Timezone

I have a weekly calendar in my application which shows events from start of the week to end of the week. The events in the backend is being stored in UTC. user might be viewing the calendar in any timezone.

My approach to handle multiple timezone here is to store the events in UTC timezone and when the call comes to the backend, get start time and end time of the week based on the user time zone(User timezone will be sent to the backend in the request header) and then convert the start time and end time to UTC timezone so as to filter all the events in the database. Finally, send all the events in UTC to UI and then let the UI convert based on user time zone.

I am little confused here if the timezone conversion to be done in UI or in the backend as my app will have to support mobile app as well. Also, Getting start time and end time based on User time zone and then convert to UTC to filter approach is correct.

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