Sublinear operators with rough kernel generated by fractional integrals   and commutators on generalized vanishing local Morrey spaces
  In this paper, we consider the norm inequalities for sublinear operators with rough kernel generated by fractional integrals and commutators on generalized local Morrey spaces and on generalized vanishing local Morrey spaces including their weak versions under generic size conditions which are satisfied by most of the operators in harmonic analysis, respectively. As an example to the conditions of these theorems are satisfied, we can consider the Marcinkiewicz operator. 
Ferit Gurbuz
math.AP