Let[inline-graphic not available: see fulltext] denote the space of all holomorphic functions on the unit ball[inline-graphic not available: see fulltext]. We investigate the following integral operators:[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext], where[inline-graphic not available: see fulltext], and[inline-graphic not available: see fulltext] is the radial derivative of[inline-graphic not available: see fulltext]. The operator[inline-graphic not available: see fulltext] can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of two classes of Riemann-Stieltjes operators from general function space[inline-graphic not available: see fulltext], which includes Hardy space, Bergman space,[inline-graphic not available: see fulltext] space, BMOA space, and Bloch space, to[inline-graphic not available: see fulltext]-Bloch space[inline-graphic not available: see fulltext] in the unit ball is discussed in this paper.