Dirichlet型空间的Carleson测度和乘子

Carleson measures and multipliers for Dirichlet type spaces in the unit ball of C^n

设0<p<∞,α>-1,D_α~p表示单位球B_n上满足∫_(B_n)(1-|z|~2)~α|▽f(z)|~pdv(z)<∞的全纯函数全体.对0<p≤q<∞,刻画了B_n上正的Borel测度μ使得D_α~p(?)L^q(dμ)和D_α~p到D_β~q的乘子.

For 0<p<∞andα>-1,let D_α~p denote the space of those functions f which are holomorphic in the unit ball B_n and satisfy∫_(B_n)(1-|z|~2)~α|▽f(z)|~Pd(z)<∞.In this paper,the positive Borel measuresμin B_n such that D_α~p(?)L^q(dμ) and the pointwise multipliers from D_α~p to D_β~q for 0<p≤q<∞are characterized.