Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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


The conjugation operator on $ A\sb q(G)$

Authors: Sanjiv Kumar Gupta, Shobha Madan and U. B. Tewari
Journal: Proc. Amer. Math. Soc. 121 (1994), 163-166
MSC: Primary 43A17; Secondary 42A50, 47B38
MathSciNet review: 1181167
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

$\displaystyle {A_q}(G) = \{ f\vert f \in {L^1}(G),\quad \hat f \in {l_q}(\Gamma )\} $

with the norm $ {\left\Vert f \right\Vert _{{A_q}}} = {\left\Vert f \right\Vert _{{L^1}}} + {\left\Vert {\hat f} \right\Vert _{{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 Young'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)$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A17, 42A50, 47B38

Retrieve articles in all journals with MSC: 43A17, 42A50, 47B38

Additional Information

PII: S 0002-9939(1994)1181167-4
Keywords: Conjugation operator, Rudin-Shapiro polynomials
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia