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.

 

$L^{p}$ multipliers with weight $x^{kp-1}$
HTML articles powered by AMS MathViewer

by Benjamin Muckenhoupt and Wo Sang Young PDF
Trans. Amer. Math. Soc. 275 (1983), 623-639 Request permission

Abstract:

Let $k$ be a positive integer and $1 < p < \infty$. It is shown that if $T$ is a multiplier operator on ${L^p}$ of the line with weight $|x{|^{kp-1}}$, then $Tf$ equals a constant times $f$ almost everywhere. This does not extend to the periodic case since $m(j) = 1/j, j \ne 0$, is a multiplier sequence for ${L^p}$ of the circle with weight $|x{|^{kp-1}}$. A necessary and sufficient condition is derived for a sequence $m(j)$ to be a multiplier on ${L^2}$ of the circle with weight $|x{|^{2k - 1}}$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 42A45
  • Retrieve articles in all journals with MSC: 42A45
Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 275 (1983), 623-639
  • MSC: Primary 42A45
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0682722-5
  • MathSciNet review: 682722