## Results on weighted norm inequalities for multipliers

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- by Douglas S. Kurtz and Richard L. Wheeden PDF
- Trans. Amer. Math. Soc.
**255**(1979), 343-362 Request permission

## Abstract:

Weighted ${L^p}$-norm inequalities are derived for multiplier operators on Euclidean space. The multipliers are assumed to satisfy conditions of the Hörmander-Mikhlin type, and the weight functions are generally required to satisfy conditions more restrictive than ${A_p}$ which depend on the degree of differentiability of the multiplier. For weights which are powers of $\left | x \right |$, sharp results are obtained which indicate such restrictions are necessary. The method of proof is based on the function ${f^\# }$ of C. Fefferman and E. Stein rather than on Littlewood-Paley theory. The method also yields results for singular integral operators.## References

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## Additional Information

- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**255**(1979), 343-362 - MSC: Primary 42A45; Secondary 42B20
- DOI: https://doi.org/10.1090/S0002-9947-1979-0542885-8
- MathSciNet review: 542885