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Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater

Authors: F. J. Martín-Reyes and E. Sawyer
Journal: Proc. Amer. Math. Soc. 106 (1989), 727-733
MSC: Primary 26A33; Secondary 26D10, 42B25
MathSciNet review: 965246
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Abstract: A simple characterization is given for two-weight norm inequalities for generalized Hardy operators $ {T_\varphi }f(x) = \smallint _0^x\varphi (\tfrac{t}{x})f(t)dt$, where $ \varphi :(0,1) \to (0,\infty )$ is nonincreasing and satisfies $ \varphi (ab) \leq D[\varphi (a) + \varphi (b)]$ for $ 0 < a,b < 1$. Included in particular are the Riemann-Liouville fractional integrals.

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Article copyright: © Copyright 1989 American Mathematical Society

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