within the sphere of influence
Used in political, military, or economic contexts to describe an area or group under someone's control or influence. Often followed by particles like に or の.
That country is within the sphere of influence of a major power.
In areas within its sphere of influence, the company's influence is strong.
Compound of 勢力圏 (sphere of influence) and 内 (within). The exact historical derivation is uncertain, but the word follows a common pattern of adding 内 to a noun to mean 'within that area or scope'.