Mixed-norm bounds for circular averages on α-dimensional fractals yield the first exceptional set estimates for Hölder regularity of linear wave solutions in R².
Ann.\@ Math.\@ (2) 136(1) (1992): 207--218
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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.
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Weighted mixed-norm estimates for circular averages and exceptional set estimates for the wave equation
Mixed-norm bounds for circular averages on α-dimensional fractals yield the first exceptional set estimates for Hölder regularity of linear wave solutions in R².
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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.