American Airlines have round trip airfares travelling from Los Angeles (LAX) to Dominican Republic (PUJ) for $397, making 1 stop. This is on American's basic economy fare. American's Basic Economy fare limits carry-on bags to one small personal item, such as a purse or laptop bag. All other baggage must be checked for a fee.
Departs LAX: Jan 16 thru Feb 9 and then Feb 13 20, 26, 27, 28; March 2, 6, 13
Returns: wide availability. Generally a 7 day minimum stay works
Use dates and book it on Expedia [expedia.com]
or American Airlines [aa.com]