The autoconvolution inequality, also called the Martin-O'Bryant autoconvolution inequality, concerns the least constant 
for which
 |
for every nonzero nonnegative function 
, where 
is the convolution of 
with itself and 
is the Lp norm. The bound with 
follows by integrating 
. Martin and O'Bryant (2009)
proposed 
, which Matolcsi and Vinuesa (2010) refuted.
Crmarić et al. (2026) showed that the ratio of the left-hand side to the product of the two norms on the right can approach 1
for nonnegative compactly supported step functions.
Thus 
is sharp. The authors credit AI with developing the proof.
