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Coefficient multipliers on Banach spaces of analytic functions. (English) Zbl 1235.42004

Motivated by the paper of J. H. Wells [J. Lond. Math. Soc., II. Ser. 2, 549–556 (1970; Zbl 0198.18102)] they define the space \(Y\otimes Y\), where \(X\) and \(Y\) are “homogeneous” Banach spaces of analytic functions on the unit disc \(\mathbb{D}\), by the requirement that \(f\) can be represented as \(f= \sum^\infty_{j=0} g_n* h_n\), with \(g_n\in X\), \(h_n\in Y\) and \[ \sum^\infty_{n=1}\| g_n\|_X\| h_n\|_Y< \infty. \] The authors show that this construction is closely related to coefficient multipliers.

MSC:

42A45 Multipliers in one variable harmonic analysis
30A99 General properties of functions of one complex variable
46E15 Banach spaces of continuous, differentiable or analytic functions
46A45 Sequence spaces (including Köthe sequence spaces)

Citations:

Zbl 0198.18102
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References:

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