The phrase "under its influence" is correct and usable in written English.
You can use it to describe something that is being affected by an outside source. For example, "The economy is struggling under its influence."
Doctors found that patients mumbled while under its influence so they started using it to treat shell shock by allowing patients to release suppressed fears and enabling them to come out of shock.
"The Beatles, Steve Jobs when he was stuck took acid; so many great works of popular art were made under its influence, so the idea that it can extend to sports is intriguing," Alexander said.
Under its influence the minority centre-right coalition it has propped up for the past decade has turned Denmark's immigration regime into one of Europe's tightest.
It was believed to bless those born under its influence with honour and riches.
But gravitational attraction is so puny that it had been tough to prove whether objects under its influence were equally restricted.
Given the widespread use of aspirin in primary and secondary cardiovascular disease preventions, it is not uncommon that patients will be under its influence during the peri-operative period.
The prevalent hypotheses for the appearance of imprinting imply that, although advantageous in some respects, it imposed a burden on bystander genes that came under its influence.
I, too, fell under its influence.
What's expensive are the decisions you make under its influence.
In the UK, 360 people have died under its influence, most with prior "non-flu" conditions.
Under its influence, he and a few friends founded "a small surrealist group called Medusa".
