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*, In Fractional Calculus, Res. Notes Math. 138, Pitman, 1985, 12-25. MR**860083 (88a:42025)****[2]**K. F. Andersen and E. Sawyer,*Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators*, to appear in Trans. A.M.S. MR**930071 (89h:26006)****[3]**L. Carleson and P. Jones,*Weighted norm inequalities and a theorem of Koosis*, Mittag-Leffler Inst. Rep. (1981).**[4]**A. Gatto and C. Gutierrez,*On weighted norm inequalities for the maximal function*, Studia Math.**76**(1983), 59-62. MR**728196 (85f:42031)****[5]**B. Muckenhoupt,*Weighted norm inequalities for classical operators*, Proc. Symp. Pure Math.**35**(1) (1979), 69-83. MR**545240 (80i:42015)****[6]**E. Sawyer,*Two weight norm inequalities for certain maximal and integral operators*, Lecture Notes in Math. 908 (1982), 102-127. MR**654182 (83k:42020b)****[7]**W. S. Young,*Weighted norm inequalities for the Hardy-Littlewood maximal function*, Proc. A.M.S.**85**(1982), 24-46. MR**647890 (84h:42033)**

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Additional Information

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

Article copyright:
© Copyright 1989
American Mathematical Society