Lacunary delta-discretised spherical maximal operators are Lp bounded for 1<p<infinity and H1 to weak L1, with constants independent of delta; the multi-parameter variant is also Lp bounded.
Christ,Weak type(1, 1) bounds for rough operators, Ann
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Lacunary $\delta$-Discretised Spherical Maximal Operators
Lacunary delta-discretised spherical maximal operators are Lp bounded for 1<p<infinity and H1 to weak L1, with constants independent of delta; the multi-parameter variant is also Lp bounded.