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Search: MSC category 42A45 ( Multipliers )

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1. CJM 2002 (vol 54 pp. 1165)

Blasco, Oscar; Arregui, José Luis
Multipliers on Vector Valued Bergman Spaces
Let $X$ be a complex Banach space and let $B_p(X)$ denote the vector-valued Bergman space on the unit disc for $1\le p<\infty$. A sequence $(T_n)_n$ of bounded operators between two Banach spaces $X$ and $Y$ defines a multiplier between $B_p(X)$ and $B_q(Y)$ (resp.\ $B_p(X)$ and $\ell_q(Y)$) if for any function $f(z) = \sum_{n=0}^\infty x_n z^n$ in $B_p(X)$ we have that $g(z) = \sum_{n=0}^\infty T_n (x_n) z^n$ belongs to $B_q(Y)$ (resp.\ $\bigl( T_n (x_n) \bigr)_n \in \ell_q(Y)$). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces $X$ and $Y$. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in $B_p(X)$ are introduced.

Categories:42A45, 46E40

2. CJM 2001 (vol 53 pp. 565)

Hare, Kathryn E.; Sato, Enji
Spaces of Lorentz Multipliers
We study when the spaces of Lorentz multipliers from $L^{p,t} \rightarrow L^{p,s}$ are distinct. Our main interest is the case when $s
Keywords:multipliers, convolution operators, Lorentz spaces, Lorentz-improving multipliers
Categories:43A22, 42A45, 46E30

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