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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Certain Schur-Hadamard multipliers in the spaces $ C\sb{p}$


Author: Jonathan Arazy
Journal: Proc. Amer. Math. Soc. 86 (1982), 59-64
MSC: Primary 47D15; Secondary 46B99, 47B10
MathSciNet review: 663866
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be a continuously differentiable function on $ [ - 1,1]$ satisfying $ \left\vert {f'(t)} \right\vert \leqslant C{\left\vert t \right\vert^\alpha }$ for some $ 0 < C$, $ \alpha < \infty $ and all $ - 1 \leqslant t \leqslant 1$, and let $ \lambda = ({\lambda _i}) \in {l_r}$ satisfy $ - 1 \leqslant {\lambda _i} \leqslant 1$ for all $ i$. Then

$\displaystyle {a_{f,\lambda }} = \left( {\frac{{f({\lambda _i}) - f({\lambda _j})}} {{{\lambda _i} - {\lambda _j}}}} \right)$

is a Schur-Hadamard multiplier from $ {C_{{p_1}}}$ into $ {C_{{p_2}}}$ for all $ {p_1}$, $ {p_2}$ satisfying $ 1 \leqslant {p_2} \leqslant 2 \leqslant {p_1} \leqslant \infty $ and $ p_2^{ - 1} \leqslant p_1^{ - 1} + \alpha /r$.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0663866-5
PII: S 0002-9939(1982)0663866-5
Keywords: $ {C_p}$ spaces, Schur-Hadamard multipliers, triangular projection
Article copyright: © Copyright 1982 American Mathematical Society