Weighted norm inequalities for fractional integrals

Author:
G. V. Welland

Journal:
Proc. Amer. Math. Soc. **51** (1975), 143-148

MSC:
Primary 26A86; Secondary 26A33

DOI:
https://doi.org/10.1090/S0002-9939-1975-0369641-X

MathSciNet review:
0369641

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Abstract: A simpler proof of an inequality of Muckenhoupt and Wheeden is given. Let be given for functions defined in . Let be a weight function which satisfies

**[1]**R. R. Coifman and C. Fefferman,*Weighted norm inequalities for maximal functions and singular integrals*, Studia Math.**51**(1974), 241-250. MR**0358205 (50:10670)****[2]**L. I. Hedberg,*On certain convolution inequalities*, Proc. Amer. Math. Soc.**36**(1972), 505-510. MR**47**#794. MR**0312232 (47:794)****[3]**B. Muckenhoupt and R. L. Wheeden,*Weighted norm inequalities for fractional integrals*, Trans. Amer. Math. Soc.**192**(1974), 261-274. MR**0340523 (49:5275)****[4]**A. Zygmund,*Trigonometric series*. Vols. I, II, 2nd ed., Cambridge Univ. Press, New York, 1959. MR**21**#6498. MR**0236587 (38:4882)****[5]**-,*A note on the differentiability of integrals*, Colloq. Math.**16**(1967), 199-204. MR**35**#1732. MR**0210847 (35:1732)**

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0369641-X

Article copyright:
© Copyright 1975
American Mathematical Society