Littlewood-Paley and multiplier theorems on weighted $L^{p}$ spaces
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- by Douglas S. Kurtz PDF
- Trans. Amer. Math. Soc. 259 (1980), 235-254 Request permission
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
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Additional Information
- © Copyright 1980 American Mathematical Society
- 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