Continuity and approximate differentiability of multisublinear fractional maximal functions

In this note we investigate the continuity and approximate differentiability of the msublinear fractional maximal operatorWe also show that the multisublinear fractional maximal functions M α ( f ) are approximately differentiable a.e. if f = ( f 1 , f 2 ,... , f m ) with each f j ∈ L 1 (R d ) being approximately differentiable a.e.As applications, the corresponding results for fractional maximal operators are established.