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

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

 

Duality between $ H\sp{p}$ and $ H\sp{q}$ and associated projections


Author: Walter Pranger
Journal: Proc. Amer. Math. Soc. 49 (1975), 342-348
MSC: Primary 30A78
MathSciNet review: 0377064
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ U/G$ represents a Riemann surface as the disk $ U$ modulo a discontinuous group $ G$ and if $ {L^p}/G$ denotes the $ {L^p}$ functions on the circle which are $ G$ invariant, then it is shown that $ {L^p}/G = {N_p} \oplus {K_p}$ if and only if $ {H^p}/G$ and $ {\bar H^q}/G$ are naturally dual. Here $ {K_p}$ is the subset of $ {L^p}/G$ consisting of those functions which are invariant and whose conjugates are invariant; $ {N_p}$ is $ E({H^p}) \cap E(\bar H_0^p)$ where $ E$ is the conditional expectation operator. $ {H^p}$ is the space of boundary values of holomorphic functions and $ 1 < p < \infty $.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A78

Retrieve articles in all journals with MSC: 30A78


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0377064-2
PII: S 0002-9939(1975)0377064-2
Article copyright: © Copyright 1975 American Mathematical Society