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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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