Two nonequivalent conditions for weight functions

Authors:
Charles Fefferman and Benjamin Muckenhoupt

Journal:
Proc. Amer. Math. Soc. **45** (1974), 99-104

MSC:
Primary 26A33; Secondary 42A40, 44A25

MathSciNet review:
0360952

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Abstract: A nonnegative function on the real line satisfies the condition if, given , there exists a such that if is an interval, , and , then . A nonnegative function on the real line satisfies the condition if for every interval , where is the interval with the same center as and twice as long, and is independent of . An example is given of a function that satisfies but not .

**[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]**Harald Cramér,*Mathematical Methods of Statistics*, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR**0016588****[3]**R. F. Gundy and R. L. Wheeden,*Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series*, Studia Math.**49**(1973/74), 107–124. MR**0352854****[4]**Benjamin Muckenhoupt,*The equivalence of two conditions for weight functions*, Studia Math.**49**(1973/74), 101–106. MR**0350297****[5]**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**[6]**Richard L. Wheeden,*On the radial and nontangential maximal functions for the disc*, Proc. Amer. Math. Soc.**42**(1974), 418–422. MR**0333194**, 10.1090/S0002-9939-1974-0333194-1

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0360952-X

Article copyright:
© Copyright 1974
American Mathematical Society