L^p Norm of a Function on $\mathbb{T}$

[Dragonfall]

Suppose \mathbb{T}=[-\pi,\pi] and we have a function in L^p(\mathbb{T}) with some measure. If we know the Fourier coefficients of f, what is the L^p norm of f? Is it (\sum f_i^p)^{1/p}? where fi are the coefs.

 

[AKG]

Is this a question about the definition of the L^p norm? For f, it would be:

\left (\int _{\mathbb{T}}|f|^p\, d\mu \right )^{\frac{1}{p}}

where \mu is the measure. Haven't looked at Fourier coefficients yet, so I can't answer your question, but I suspect what you put is wrong because it's missing absolute value signs.