A note on two weight function conditions for a Fourier transform norm inequality
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- by Benjamin Muckenhoupt
- Proc. Amer. Math. Soc. 88 (1983), 97-100
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691285-5
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Abstract:
Recent papers have given two different conditions on pairs of nonnegative weight functions that insure that a Fourier transform norm inequality holds in ${{\mathbf {R}}^n}$. With additional assumptions these conditions were also shown to be implied by the norm inequality. A direct proof is given here that these conditions are equivalent; this can be used to simplify some of the proofs in those papers.References
- Hans P. Heinig, Weighted norm inequalities for classes of operators, Indiana Univ. Math. J. 33 (1984), no. 4, 573–582. MR 749315, DOI 10.1512/iumj.1984.33.33030
- W. B. Jurkat and G. Sampson, On rearrangement and weight inequalities for the Fourier transform, Indiana Univ. Math. J. 33 (1984), no. 2, 257–270. MR 733899, DOI 10.1512/iumj.1984.33.33013
- Benjamin Muckenhoupt, Weighted norm inequalities for the Fourier transform, Trans. Amer. Math. Soc. 276 (1983), no. 2, 729–742. MR 688974, DOI 10.1090/S0002-9947-1983-0688974-X
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 97-100
- MSC: Primary 42A45; Secondary 42A50
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691285-5
- MathSciNet review: 691285