Fourier inequalities with nonradial weights

Author:
C. Carton-Lebrun

Journal:
Trans. Amer. Math. Soc. **333** (1992), 751-767

MSC:
Primary 42B10; Secondary 26D10, 47G10

MathSciNet review:
1132433

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Abstract: Let , and , be nonnegative functions. Sufficient conditions are found in order that for all . Pointwise and norm approximations of are derived. Similar results are obtained when is replaced by a measure weight. In the case , a counterexample is given which shows that no Fourier inequality can hold for all in . Spherical restriction theorems are established. Further conditions for the boundedness of are discussed.

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1132433-2

Article copyright:
© Copyright 1992
American Mathematical Society