4. Integrable square functions

4.1 Plancherel's theorem

The Fourier transformation on $L^{1} (ℝ)$ is not without its drawbacks. It can only be reasonably inverted if $\hat{f}$ is itself integrable, which is not always easy to decide; we would like to define it on $L^{2} (ℝ)$ ...

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Integrable square functions

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References

(1) - DYM (H.), MC KEAN (H.P.) - Fourier Series and Integrals. - Academic Press 1972.
(2) - FOLLAND (G.) - Introduction to partial differential equations. - Princeton University Press 1976.
(3)...

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