Weighted weak-type (1, 1) estimates for radial Fourier multipliers via extrapolation theory

Abstract

In this paper, we prove a weighted estimate for the Bochner–Riesz operator at the critical index that is stronger than the weak-type (1,1) for A1 weights, in the sense that the latter can be obtained via extrapolation arguments from the former. In addition, this estimate can be transferred to averages in order to deduce weighted weak-type (1,1) results for general radial Fourier multipliers.