With inner product $\langle f,g\rangle=\int_0^{2\pi}f(t)\overline{g(t)}dt$ on $L_2[0,2\pi]$ how do $||f||$, $||f||_2$ and $\langle f,f\rangle$ relate?

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With inner product $\langle f,g\rangle=\int_0^{2\pi}f(t)\overline{g(t)}dt$ on $L_2[0,2\pi]$ how do $||f||$, $||f||_2$ and $\langle f,f\rangle$ relate?

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