Weighted norm inequalities for the Fourier transform

Author:
Benjamin Muckenhoupt

Journal:
Trans. Amer. Math. Soc. **276** (1983), 729-742

MSC:
Primary 42A38; Secondary 26D15, 42B10, 44A15

DOI:
https://doi.org/10.1090/S0002-9947-1983-0688974-X

MathSciNet review:
688974

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Abstract | References | Similar Articles | Additional Information

Abstract: Given and satisfying , sufficient conditions on nonnegative pairs of functions are given to imply

**[1]**Néstor E. Aguilera and Eleonor O. Harboure,*On the search for weighted norm inequalities for the Fourier transform*, Pacific J. Math.**104**(1983), no. 1, 1–14. MR**683723****[2]**Björn E. J. Dahlberg,*Regularity properties of Riesz potentials*, Indiana Univ. Math. J.**28**(1979), no. 2, 257–268. MR**523103**, https://doi.org/10.1512/iumj.1979.28.28018**[3]**Peter Knopf and Karl Rudnick,*Weighted norm inequalities for the Fourier transform*(preprint).**[4]**Benjamin Muckenhoupt,*Weighted norm inequalities for classical operators*, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 69–83. MR**545240****[5]**Y. Sagher,*Real interpolation with weights*, Indiana Univ. Math. J.**30**(1981), no. 1, 113–121. MR**600037**, https://doi.org/10.1512/iumj.1981.30.30010**[6]**Elias M. Stein,*Interpolation of linear operators*, Trans. Amer. Math. Soc.**83**(1956), 482–492. MR**0082586**, https://doi.org/10.1090/S0002-9947-1956-0082586-0**[7]**Elias M. Stein,*Singular integrals and differentiability properties of functions*, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR**0290095****[8]**Elias M. Stein and Guido Weiss,*Introduction to Fourier analysis on Euclidean spaces*, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR**0304972**

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0688974-X

Article copyright:
© Copyright 1983
American Mathematical Society