What's the Fourier transform of a multivariable function

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Let's say I have a P that depends on t: P(t). I also have function C, which depends on P(t) and indirectly on t: C(P(t), t). I know that the Fourier Transform of P(t) would be P(w). What would be the transformation of C in general to the frequency domain? (Note: I am looking for the general case where the dependence of C on P has not been defined.... is there any mathematical relation to taking the Fourier transform of C)?