Short answer, no.
The means of production - big and small - are collectively owned by the whole working class, or in classless social societies, by everyone. That said, in practice it's very likely that in some cases the main decisions about the use of certain small concentrations of productive resources will be made by a few or even a single person. That is, there may well be people who do many similar things as some small businesspeople in capitalist societies, but they won't privately own the businesses in the same way one would in a capitalist society.


