Gradient estimates and Jackson’s theorem in QμQμ spaces related to measures

Jackson’s theorem is established in a new kind of holomorphic function space QμQμ related to measures in any starlike circular domain in CnCn. Particularly, the result covers many spaces including BMOABMOA, QpQp, QKQK, and F(p,q,s)F(p,q,s) spaces in the unit ball of CnCn. Moreover, we construct integral operators which give pointwise estimates for the gradient of the difference in terms of the gradient on the boundary. The gradient estimates are independent of the measures in question and give rise to Jackson’s theorem.