For any A subset of reals with Hausdorff dimension s in (0,1/2], either upper box dim(AA) or lower box dim(A+A) is at least 29s/23 (or 33s/26 for differences).
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A note on the sum-product problem for fractal sets
For any A subset of reals with Hausdorff dimension s in (0,1/2], either upper box dim(AA) or lower box dim(A+A) is at least 29s/23 (or 33s/26 for differences).