Skip to Main Content

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.

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.

 

Weighted norm inequalities for Hilbert transforms and conjugate functions of even and odd functions
HTML articles powered by AMS MathViewer

by Kenneth F. Andersen PDF
Proc. Amer. Math. Soc. 56 (1976), 99-107 Request permission

Abstract:

It is well known that the Hilbert tranformation and the conjugate function operator restricted to even (odd) functions define bounded linear operators on weighted ${L^p}$ spaces under more general conditions than is the case for the unrestricted operators. In analogy with recent results of Hunt, Muckenhoupt and Wheeden for the Hilbert transform and the conjugate function operator, we obtain necessary and sufficient conditions in order that these restricted operators should satisfy weighted weak-type inequalities and hence also necessary and sufficient conditions in order that these operators should be bounded on weighted ${L^p}$ spaces for $1 < p < \infty$.
References
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 99-107
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0399739-2
  • MathSciNet review: 0399739