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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1980-0561835-X
MathSciNet review: 561835
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0561835-X
Keywords: Multipliers, weight functions, partial sum operators
Article copyright: © Copyright 1980 American Mathematical Society

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