Weighted norm inequalities of the maximal commutator of quasiradial Bochner-Riesz operators

Abstract

In this paper, we obtain certain L (w) (p) (a"e (n) )-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index delta under certain surface condition on I pound (I +/- d) , provided that delta > (n - 1)/2, b a BMO(a"e (n) ), 1 < p < a and w a A (1). Moreover, if delta > (n - 1)/2, then we prove that the above maximal operator admits weak type (H (w) (1) (a"e (n) ), L (w) (1) (a"e (n) ))-mapping properties for b a BMO(a"e (n) ) and w a A (1) under the surface condition on I pound (I +/- d) .