I am interested in conditions on $f: \mathbb{R}^d \rightarrow \mathbb{R}$ that lead to decay of the Fourier transform of $f$. A standard one is $f\in C^k$ and $\partial^\alpha f \in L^1$ for $\vert \alpha \vert \leq k$ leads to $\vert \hat{f}(p) \vert \leq C (1+ \vert p \vert)^{-k}$ (Decay rate of the Fourier transform). Another example is that if $f$ is bounded, integrable and of bounded variation, then $\hat{f}(p) = o(\vert p \vert^{-1})$. So my question is
Can you recommend a source where I can find estimates for the Fourier transform based on regularity conditions as above.
I am mostly interested in the situation when $f$ is a function and conditions of the type: If $f$ (or $\partial^\alpha f$) in $C^{k,\alpha}(\mathbb{R}^d)$, $W^{l,p}(\mathbb{R}^d)$, $BV(\mathbb{R}^d)$ $...$ then $\vert \hat{f}(p) \vert \leq \ ...$