# Norm of a function

1. Apr 1, 2007

### 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.

2. Apr 1, 2007

### AKG

Is this a question about the definition of the Lp 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.