COEFFICIENT MULTIPLIERS OF H-P SPACES OVER BOUNDED SYMMETRICAL DOMAINS IN C-N

One way to give information about the Taylor coefficients of HP functi ons is to describe the multipliers of H-p into various spaces. In the case of one complex variable, Duren and shields described the multipli ers of H-p into l(q) (0<p<1, p less than or equal to q less than or eq ual to infinity). The Duren-Shields theorems to the case with the boun ded symmetric domains in C-n are generalized. The results are sharp if q greater than or equal to 2. A sufficient condition of HP into H-q i s given for any p and q, 0<p<q infinity.