Skip to Main Content

Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Coefficient multipliers of Bloch functions
HTML articles powered by AMS MathViewer

by J. M. Anderson and A. L. Shields PDF
Trans. Amer. Math. Soc. 224 (1976), 255-265 Request permission

Abstract:

The class $\mathcal {B}$ of Bloch functions is the class of all those analytic functions in the open unit disc for which the maximum modulus is bounded by $c/(1 - r)$ on $|z| \leqslant r$. We study the absolute values of the Taylor coefficients of such functions. In particular, we find all coefficient multipliers from ${l^p}$ into $\mathcal {B}$ and from $\mathcal {B}$ into ${l^p}$. We find the second KΓΆthe dual of $\mathcal {B}$ and show its relevance to the multiplier problem. We identify all power series $\sum {a_n}{z^n}$ such that $\sum {w_n}{a_n}{z^n}$ is a Bloch function for every choice of the bounded sequence $\{ {w_n}\}$. Analogous problems for ${H^p}$ spaces are discussed briefly.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A78
  • Retrieve articles in all journals with MSC: 30A78
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 224 (1976), 255-265
  • MSC: Primary 30A78
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0419769-6
  • MathSciNet review: 0419769