## Fefferman’s ball multiplier counterexample

In the previous post we saw the connection between the ball multiplier and spherical convergence of Fourier transforms. Recall that the operator is defined in dimensions by the relation

where denotes the -dimensional unit ball. The focus of this post will be to prove the following result

**Theorem 1** (Fefferman, 1971) The operator is not bounded on if and .

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