Measure, Integration & Real Analysis · Problem 11C.16

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · fourier-transform-L2-membership

Problem

Suppose

f \in L^1(\mathbf{R})

and

\hat{f} \in L^1(\mathbf{R})

. Prove that

f \in L^2(\mathbf{R})

and

\hat{f} \in L^2(\mathbf{R})