Abstract
Given a set E⊂(0,∞), the spherical maximal operator associated to the parameter set E is defined as the supremum of the spherical means of a function when the radii of the spheres are in E. The aim of the paper is to study boundedness properties of these operators on the spaces Lp(|x|α). It is shown that the range of values of α for which boundedness holds behaves essentially as follows: (i) for p>n/(n−1) and negative α the range does not depend on E; (ii) when α is positive it depends only on the Minkowski dimension of E; (iii) if p<n/(n−1) and α is negative, sets with the same Minkowski dimension can give different ranges of boundedness.
Citation
Javier Duoandikoetxea. Edurne Seijo. "Weighted inequalities for some spherical maximal operators." Illinois J. Math. 46 (4) 1299 - 1312, Winter 2002. https://doi.org/10.1215/ijm/1258138481
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