By applying the vector-valued inequalities for the Littlewood-Paley operators and their commutators on Lebesgue spaces with variable exponent, the boundedness of the Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g μ *-functions, and their commutators generated by BMO functions, is obtained on the Morrey spaces with variable exponent.

We propose results on interior Morrey, BMO and Hölder regularity for the strong solutions to linear elliptic systems of order 2b with discontinuous coefficients and right-hand sides belonging to the Morrey space L. 1. Main Results It is well known that, when dealing with elliptic systems, in contrast to the case of a single second-order elliptic equation, the solely essential boundedness of the...

Double system of exponents with complex-valued coefficients is considered. Under some conditions on the coefficients, we prove that if this system forms a basis for the Morrey-Lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.