Boundedness of intrinsic square functions and commutators on generalized central Morrey spaces

In this paper, the authors establish the boundedness for a large class of intrinsic square functions G(alpha), g(alpha), g(lambda,alpha)(*) and their commutators [b, G(alpha)], [b, g(alpha)] and [b, g(lambda,alpha)(*)] generated with lambda-central BMO functions b epsilon CBMOp,lambda (R-n) on generalized central Morrey spaces B-q,B-theta(R-n) for 1 < q < infinity, 0 < alpha <= 1, respectively. All of the results are new even on the central Morrey spaces B-q,B-lambda (R-n).