Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Littlewood-Paley and multiplier theorems on weighted $ L\sp{p}$ spaces

Author: Douglas S. Kurtz
Journal: Trans. Amer. Math. Soc. 259 (1980), 235-254
MSC: Primary 42B25; Secondary 42B15
MathSciNet review: 561835
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Littlewood-Paley operator $ \gamma (f)$, for functions f defined on $ {{\textbf{R}}^n}$, is shown to be a bounded operator on certain weighted $ {L^p}$ spaces. The weights satisfy an $ {A_p}$ condition over the class of all n-dimensional rectangles with sides parallel to the coordinate axes. The necessity of this class of weights demonstrates the 1-dimensional nature of the operator. Results for multipliers are derived, including weighted versions of the Marcinkiewicz Multiplier Theorem and Hörmander's Multiplier Theorem.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B25, 42B15

Retrieve articles in all journals with MSC: 42B25, 42B15

Additional Information

Keywords: Multipliers, weight functions, partial sum operators
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society