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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The conjugation operator on $A_ q(G)$
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by Sanjiv Kumar Gupta, Shobha Madan and U. B. Tewari PDF
Proc. Amer. Math. Soc. 121 (1994), 163-166 Request permission

Abstract:

Let G be a compact abelian group and $\Gamma$ its dual. For $1 \leq q < \infty$, the space ${A_q}(G)$ is defined as \[ {A_q}(G) = \{ f|f \in {L^1}(G),\quad \hat f \in {l_q}(\Gamma )\} \] with the norm ${\left \| f \right \|_{{A_q}}} = {\left \| f \right \|_{{L^1}}} + {\left \| {\hat f} \right \|_{{l_q}}}$. We prove: Let G be a compact, connected abelian group and P any fixed order on $\Gamma$. If $q > 2$ and $\phi$ is a Youngā€™s function, then the conjugation operator H does not extend to a bounded operator from ${A_q}(G)$ to the Orlicz space ${L^\phi }(G)$.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 163-166
  • MSC: Primary 43A17; Secondary 42A50, 47B38
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1181167-4
  • MathSciNet review: 1181167