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

Abstract: Jackson’s theorem is established in a new kind of holomorphic function space related to measures in any starlike circular domain in . Particularly, the result covers many spaces including , , , and spaces in the unit ball of . 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. [Copyright &y& Elsevier]