H(P) MULTIPLIERS ON BOUNDED SYMMETRICAL DOMAINS

The following results are obtained in this paper: (i) if 0 < p less-th an-or-equal-to 2 less-than-or-equal-to q < infinity, alpha = 1/p - 1/q , and lambda(k) = O(k(-nalpha)), then {lambda(k)} is a multiplier of H (p)(OMEGA) into H(q)(OMEGA); (ii) if 0 < p < q < 2 and alpha = 1/p - 1 /q, then there is a sequence {lambda(k)} with lambda(k) = O(k(-nalpha) ) which is not a multiplier of H(p)(B) into H(q)(B); (iii) if 2 < p < q < infinity and alpha = 1/p - 1/q, then there is a sequence {lambda(k )} with lambda(k) = O(k(-nalpha)) which is not a multiplier of H(p)(B) into H(q)(B).