Weighted inequality on the Hardy-Littlewood maximal function is completely
understood while it is not well understood for the spherical maximal function.
For the power weight β£xβ£Ξ±, it is known that the spherical maximal
operator on Rd is bounded on Lp(β£xβ£Ξ±) only if 1βdβ€Ξ±<(dβ1)(pβ1)βd and under this condition, it is known to be bounded except
Ξ±=1βd. In this paper, we prove the case of the critical order,
Ξ±=1βd.Comment: 14 page