"popular influence" is correct and usable in written English.
You can use this phrase when referring to the impact that celebrities or public figures have on their fans or followers. For example, "The popular influence of this celebrity has led to a surge in sales of the product they endorsed."
"He was an old-fashioned, practical musician, a conductor-slash-composer, with lots of popular influence.
Even so, by 1880 Spencer's American followers had declared victory over Darwin in the race for popular influence.
In the game of move and countermove for popular influence in the villages of Nawa, the aid had vanished again.
In Thailand's constitutional monarchy, the king does not have a formal political role, but he wields enormous popular influence.
The inside of a celebrity's closet, the unveiling of rows of bottles and jars, will hardly penetrate character or unravel the riddle of popular influence.
Indeed, it's a sign of Farrakhan's oddly lasting hold on popular influence that he was even invited to clink drinks with the members of the C.B.C.
Yet as a highly acclaimed American composer, Mr. Adams has often acknowledged an openness to popular influences on his classical roots and post-Minimalist aesthetic.
The 10-minute work, which is to have its New Jersey premiere on Oct. 2 under the baton of Marco Parisotto, abounds in high energy and popular influences.
Popular influences of a more antique strain animate the "Azerbaijani Dance" (2005), a brief, assertive showpiece that examines a folk theme through the lens of splashy pianism.
On the contrary, Moranbong are North Korea's first girl band, and a sign of how open the country has become to western popular influences.
This attempt to reconceive the Met as an institution more open to popular influences and more attractive to a wider public may well alarm opera traditionalists, who are the heart of the Met's audience.
