Holomorphic functions on the mixed norm spaces on the polydisc

다국어 초록 (Multilingual Abstract)

We generalize several integral inequalities for analytic functions
on the open unit polydisc Un = {z ∈ Cn ||z|| < 1, j = 1,...,n}. It
is shown that if a holomorphic function on Un belongs to the mixed norm
space [수식], where wj(ㆍ), j = 1,..., n, are admissible weights, then
all weighted derivations of order |k| (with positive orders of derivations)
belong to a related mixed norm space. The converse of the result is proved
when, p, q ∈ [1, ∞) and when the order is equal to one. The equivalence
of these conditions is given for all p, q ∈ (0, ∞) if wj (zj) = (1 - |zj|²)αj,
αj > -1, j = 1,..., n (the classical weights.) The main results here improve
our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577–587
and Z. Anal. Anwendungen 23 (2004), no. 4, 775–782.

다국어 초록 (Multilingual Abstract)

We generalize several integral inequalities for analytic functions
on the open unit polydisc Un = {z ∈ Cn ||z|| < 1, j = 1,...,n}. It
is shown that if a holomorphic function on Un belongs to the mixed norm
space [수식], where wj(ㆍ), j = 1,..., n, are admissible weights, then
all weighted derivations of order |k| (with positive orders of derivations)
belong to a related mixed norm space. The converse of the result is proved
when, p, q ∈ [1, ∞) and when the order is equal to one. The equivalence
of these conditions is given for all p, q ∈ (0, ∞) if wj (zj) = (1 - |zj|²)αj,
αj > -1, j = 1,..., n (the classical weights.) The main results here improve
our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577–587
and Z. Anal. Anwendungen 23 (2004), no. 4, 775–782.

참고문헌 (Reference)

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