Lacunary δ‐Discretized Spherical Maximal Operators

We study the lacunary analog of the ‐discretized spherical maximal operators introduced by Hickman and Jančar, for , and establish the boundedness on for all , along with the endpoint weak‐type estimate . We also prove the corresponding boundedness for the multi‐parameter variant. The constants in these bounds are uniform in , and thus, by taking the limit , our results recover the classical boundedness of the lacunary spherical maximal function.