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]**N. E. Aguilera and E. O. Harboure,*On the search of weighted norm inequalities for the Fourier transform*(to appear). MR**683723 (85e:42007)****[2]**B. Dahlberg,*Regularity properties of Riesz potentials*, Indiana Univ. Math. J.**28**(1979), 257-268. MR**523103 (80g:31004)****[3]**Peter Knopf and Karl Rudnick,*Weighted norm inequalities for the Fourier transform*(preprint).**[4]**B. Muckenhoupt,*Weighted norm inequalities for classical operators*, Proc. Sympos. Pure Math., vol. 35, part 1, Amer. Math. Soc., Providence, R. I., 1979, pp. 69-83. MR**545240 (80i:42015)****[5]**Y. Sagher,*Real interpolation with weights*, Indiana Univ. Math. J.**30**(1981), 113-121. MR**600037 (82e:46045)****[6]**E. Stein,*Interpolation of linear operators*, Trans. Amer. Math. Soc.**83**(1956), 482-492. MR**0082586 (18:575d)****[7]**-,*Singular integrals and differentiability properties of functions*, Princeton Univ. Press, Princeton, N. J., 1970. MR**0290095 (44:7280)****[8]**E. Stein and G. Weiss,*Introduction to Fourier analysis on Euclidean spaces*, Princeton Univ. Press, Princeton, N. J., 1971. MR**0304972 (46:4102)**

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

Article copyright:
© Copyright 1983
American Mathematical Society