Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions [article]

Adam Nowak, Luz Roncal, Tomasz Z. Szarek
We find ultimate sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions to be bounded on power-weighted Lebesgue spaces. Moreover, we also obtain all the corresponding endpoint results, which are optimal power-weighted weak or restricted weak type estimates. These results shed new light on the problem of optimality of the known $L^p$ estimates for the maximal operator in the general non-radial case.
doi:10.48550/arxiv.2201.00327 fatcat:n7p6ru46dzhurlsorjwcdw4voi