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Bochner-Riesz Conjecture

The Bochner-Riesz conjecture asserts that the Bochner-Riesz mean B_R^delta is bounded on L^p(R^n), uniformly in R>0, whenever

delta>max{n|1/p-1/2|-1/2,0}.

The usual conjectural range has 1<p<infty. The strict inequality requires a positive order even when the displayed threshold is zero.

In dimension 3, the displayed threshold is zero for p=3 and p=3/2, while it is 1 for p=1 and p=infty.

See also

Bochner-Riesz Mean, Fourier Multiplier, Fourier Restriction Conjecture

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References

Stein, E. M. Harmonic Analysis. Princeton, NJ: Princeton University Press, 1993.

Cite this as:

Weisstein, Eric W. "Bochner-Riesz Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bochner-RieszConjecture.html

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