Introductory linguistics texts and History of English Courses usually cover this in a paragraph or two before moving on to discussions of how African-American Vernacular is not a substandard English, but a dialect, and all the other political statements academics feel should be inculcated into adolescents, who would otherwise have only the narrow views of their bigoted culture to fall back on. Then linguists get distracted into talking about black slang, Gullah dialect, literacy, and other topics which are important in themselves, but don’t tell us too much about the influence of African-Americans on our everyday language.
That paragraph usually gives a word list of terms that we get from African-Americans, like jazz, or yam, or banjo. This always struck me as a terribly condescending, everybody-gets-a-ribbon way to proceed. Did you know that several important words come from Turkish?!
The actual influence of black speakers is deeper and more profound. We have many small words in English that get enormous use, such as run, get, set, and go. Go up. Go over. Go for. Get through a crisis. Get under your skin. Get down tonight. Run up. Run out. Set up. Set out. We use dozens of idiomatic, nuanced versions of these words. Many of them have histories long before slaves were brought to America, but their use was not so extensive as it is today.
When wave after wave of people come in and learn your language as a second language, basic words tend to take on multiple uses. New speakers draw from what they already know to communicate. If you have the idea of run already in memory, then you are going to pick up the ideas of run out of water, run out on your wife more easily than emptied, or abandoned.
The French, Dutch, and Spanish all came early to America, but didn’t tend to learn English. Jews, Germans, Armenians, and Cambodians came in their own times and reinforced this pattern of multiple-use basic words. But it was the enormous number of Africans learning English as adults which originally gave American this idiomatic twist.
Anticipating objections: Yes, British English also uses these forms. It’s a long discussion, and I still stand by the above