HARDY-TYPE OPERATORS IN LORENTZ-TYPE SPACES DEFINED ON MEASURE SPACES

Weight criteria for the boundedness and compactness of generalized Hardy-type operators Tf(x) = u(1)(x) integral({phi(y)<=psi(x)})f(y)u(2)(y)v(0)(y)d mu(y), x is an element of X, (0.1) in Orlicz-Lorentz spaces defined on measure spaces is investigated where the functions phi, psi, u(1), u(2), v(0) are positive measurable functions. Some sufficient conditions of boundedness of T : Lambda(G0)(v0) (w(0)) -> Lambda(G1)(v1) (w(1)) and T : Lambda(G0)(v0) (w(0)) -> Lambda(G1,infinity)(v1) (w(1)) are obtained on Orlicz-Lorentz spaces. Furthermore, we achieve sufficient and necessary conditions for T to be bounded and compact from a weighted Lorentz space Lambda(p0)(v0) (w(0)) to another Lambda(p1,q1)(v1) (w(1)). It is notable that the function spaces concerned here are quasi-Banach spaces instead of Banach spaces.