On weighted norm inequalities for positive linear operators

Authors:
R. Kerman and E. Sawyer

Journal:
Proc. Amer. Math. Soc. **105** (1989), 589-593

MSC:
Primary 26D15; Secondary 26A33, 44A10, 47B38

DOI:
https://doi.org/10.1090/S0002-9939-1989-0947314-X

MathSciNet review:
947314

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a positive linear operator defined for nonnegative functions on a -finite measure space . Given and a nonnegative weight function on , it is shown that there exists a nonnegative weight function , finite -almost everywhere on , such that (1)

**[1]**K. F. Andersen,*Weighted inequalities for fractional integrals*, Fractional calculus (Glasgow, 1984) Res. Notes in Math., vol. 138, Pitman, Boston, MA, 1985, pp. 12–25. MR**860083****[2]**K. F. Andersen and E. T. Sawyer,*Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators*, Trans. Amer. Math. Soc.**308**(1988), no. 2, 547–558. MR**930071**, https://doi.org/10.1090/S0002-9947-1988-0930071-4**[3]**L. Carleson and P. Jones,*Weighted norm inequalities and a theorem of Koosis*, Mittag-Leffler Inst. Rep. (1981).**[4]**Angel E. Gatto and Cristian E. Gutiérrez,*On weighted norm inequalities for the maximal function*, Studia Math.**76**(1983), no. 1, 59–62. MR**728196**, https://doi.org/10.4064/sm-76-1-59-62**[5]**Benjamin Muckenhoupt,*Weighted norm inequalities for classical operators*, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 69–83. MR**545240****[6]**Eric T. Sawyer,*Two weight norm inequalities for certain maximal and integral operators*, Harmonic analysis (Minneapolis, Minn., 1981) Lecture Notes in Math., vol. 908, Springer, Berlin-New York, 1982, pp. 102–127. MR**654182****[7]**Wo Sang Young,*Weighted norm inequalities for the Hardy-Littlewood maximal function*, Proc. Amer. Math. Soc.**85**(1982), no. 1, 24–26. MR**647890**, https://doi.org/10.1090/S0002-9939-1982-0647890-4

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0947314-X

Article copyright:
© Copyright 1989
American Mathematical Society