Boundedness of vector-valued Calderon-Zygmund operators on non-homogeneous metric measure spaces

Let (chi, d, mu) be a non-homogeneous metric measure space and satisfies non-atomic condition that mu({x}) = 0 for all x is an element of chi, B-1 and B-2 are Banach spaces. In this paper, we show that the boundedness of the vector-valued Calderon-Zygmund operator (T) over right arrow from L-2(chi, B-1) to L-2(chi, B-2) is equivalent to (T) over right arrow from L-p(chi, B-1) to L-p(chi, B-2) for p is an element of (1, infinity), and from L-1(chi, B-1) to L-1,L-infinity (chi, B-2). As an application, we prove that if (T) over right arrow is bounded from L-2(chi, B-1) to L-2(chi, B-2), then its maximal operator is bounded from L-p(chi, B-1) to L-p(chi, B-2) for p is an element of (1, infinity) and from L-1(chi, B-1) to L-1,L-infinity (chi, B-2).