Riesz Potential, Marcinkiewicz Integral and Their Commutators on Mixed Morrey Spaces

This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b,I-alpha], where I-alpha denotes the fractional integral operator of order alpha and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b, I-alpha](k) are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral mu(Omega) and the commutator [b,mu(Omega)] when b belongs to the BMO class.