Weighted norm inequalities for fractional integrals

Author:
G. V. Welland

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

MSC:
Primary 26A86; Secondary 26A33

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****[2]**Lars Inge Hedberg,*On certain convolution inequalities*, Proc. Amer. Math. Soc.**36**(1972), 505–510. MR**0312232**, 10.1090/S0002-9939-1972-0312232-4**[3]**Benjamin Muckenhoupt and Richard Wheeden,*Weighted norm inequalities for fractional integrals*, Trans. Amer. Math. Soc.**192**(1974), 261–274. MR**0340523**, 10.1090/S0002-9947-1974-0340523-6**[4]**A. Zygmund,*Trigonometric series: Vols. I, II*, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968. MR**0236587****[5]**A. Zygmund,*A note on the differentiability of integrals*, Colloq. Math.**16**(1967), 199–204. MR**0210847**

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

Article copyright:
© Copyright 1975
American Mathematical Society