Necessity conditions for $L^ p$ multipliers with power weights
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- by Benjamin Muckenhoupt PDF
- Trans. Amer. Math. Soc. 300 (1987), 503-520 Request permission
Abstract:
It is shown that if multiplier operators are bounded on with weight ${\left | x \right |^\alpha }$ for all functions in the space ${\mathcal {S}_{0,0}}$ of Schwartz functions whose Fourier transforms have compact support not including 0 and all multiplier functions in a standard Hörmander type multiplier class, then $\alpha$ must satisfy certain inequalities. This is a sequel to a previous paper in which conditions on $\alpha$ that were almost the same were shown to be sufficient for the norm inequality to hold.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 300 (1987), 503-520
- MSC: Primary 42A45; Secondary 42B15
- DOI: https://doi.org/10.1090/S0002-9947-1987-0876463-2
- MathSciNet review: 876463