For radial functions, the paper determines the full Lp-improving region for spherical maximal operators over fractal dilation sets in dimensions d≥3, and for quasi-Assouad regular sets in d=2.
Classes of singular integral operators along variable lines
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$L^p$-improving bounds for spherical maximal operators over restricted dilation sets: radial improvement
For radial functions, the paper determines the full Lp-improving region for spherical maximal operators over fractal dilation sets in dimensions d≥3, and for quasi-Assouad regular sets in d=2.