From the Super Mario Wiki
Dozing Sands is the desert area that appears in Mario & Luigi: Dream Team. On Pi'illo Island, it is on the bottom right corner. Many Brocks here mine with their boss, Britta, in order to turn the area into a tourist attraction.
Mario and Luigi head here after Antasma and Bowser say they will take the Dream Stone and make it grant their wishes. The Dream Stone is supposedly held here in Dozing Sands. Mario and Luigi learn that they must save the Pi'illo Keepers in order to progress up the large sand-flow where the Dream Stone may possibly be. After making their way up there, Mario and Luigi save Britta when she's attacked by Torkscrew by defeating him. Afterwards, they find the Dream Point where the Dream Stone was and enter Dreamy Dozing Sands to hopefully find out the location of the Dream Stone.
Names in other languages
If the player returns to the area where the four Zeekeeper statues are, one of the workers will sing about working and his final words are 'down from Donut Plains to Jolly Roger Bay', referencing Super Mario World and Super Mario 64.