Under the stated ranges for k, d and p, the maximal operator given by the sup over r of the absolute value of r^k times the k-th derivative of the spherical mean is bounded on L^p with a bound independent of dimension d.
Ann.\@ Math.\@ (2) 182(1) (2015): 351--389
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Maximal inequalities for derivatives of spherical means
Under the stated ranges for k, d and p, the maximal operator given by the sup over r of the absolute value of r^k times the k-th derivative of the spherical mean is bounded on L^p with a bound independent of dimension d.