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Zbl 0664.26002
Andersen, K.F.; Sawyer, E.T.
Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators.
(English)
[J] Trans. Am. Math. Soc. 308, No.2, 547-558 (1988). ISSN 0002-9947; ISSN 1088-6850/e

This paper studies weighted norm inequalities $$[\int\sp{\infty}\sb{0}\vert (Tf)(x)u(x)\vert\sp q dx]\sp{1/q}\le C[\int\sp{\infty}\sb{0}\vert f(x)v(x)\vert\sp p dx]\sp{1/p},$$ where u and v are nonnegative weight functions, $\alpha >0,\quad 1<p<1/\alpha,\quad 1/q=1/p-\alpha,$ and C is a constant depending on p, q, $\alpha$, u, v but independent of f and T is one of Riemann-Liouville or Weyl fractional integral from which inequalities for other fractional integral operators T, such as Erdélyi-Kober, can be deduced. Some questions raised by {\it B. Muckenhoupt} [Proc. Symp. Pure Math. 35, No.1, 69-83 (1979; Zbl 0428.26009)] have been answered through Theorems 2 and 3.
[R.N.Kalia]
MSC 2000:
*26A33 Fractional derivatives and integrals (real functions)
26D10 Inequalities involving derivatives, diff. and integral operators
42B25 Maximal functions

Keywords: Riemann-Liouville fractional integrals; weighted norm inequalities; Weyl fractional integral

Citations: Zbl 0428.26009

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