COMMUTATORS OF CONVOLUTION TYPE OPERATORS ON SOME BANACH FUNCTION SPACES

We study the boundedness of Fourier convolution operators W-0 (b) and the compactness of commutators of W-0 (b) with multiplication operators al on some Banach function spaces X (14) for certain classes of piecewise quasicontinuous functions a is an element of PQC and piecewise slowly oscillating Fourier multipliers b is an element of PSO degrees(X,1). We suppose that X( I) is a separable rearrangement-invariant space with nontrivial Boyd indices or a reflexive variable Lebesgue space, in which the Hardy Littlewood maximal operator is bounded. Our results complement those of Isaac De La Cruz Rodriguez, Yuri Karlovich, and Ivan Loreto Hernandez obtained for Lebesgue spaces with Muckenhoupt weights.