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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1997 • Question 3

Question

Math 6210 • Real Analysis Fall 1997 • Question 3

Suppose that \(f\in L^1(\mathbb R^n)\) and \(\hat f\in L^1(\mathbb R^n)\) (\(\hat f\) denoting the Fourier transform of \(f\)). Then show that \[ f\in L^1(\mathbb R^n)\cap L^2(\mathbb R^n). \]

Raw LaTeX

Suppose that \(f\in L^1(\mathbb R^n)\) and
\(\hat f\in L^1(\mathbb R^n)\) (\(\hat f\) denoting the Fourier transform of \(f\)).
Then show that
\[
f\in L^1(\mathbb R^n)\cap L^2(\mathbb R^n).
\]

Topic Tags

Fourier Analysis and Convolution Lp Spaces and Sequence Spaces