Linear monotone operators and weighted BMO

Author:
Qinsheng Lai

Journal:
Proc. Amer. Math. Soc. **120** (1994), 875-887

MSC:
Primary 42B99; Secondary 47B38

DOI:
https://doi.org/10.1090/S0002-9939-1994-1169887-9

MathSciNet review:
1169887

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Abstract: In this paper, the linear monotone operators, which include the well-known Hardy operator and Riemann-Liouville fractional integrals, are introduced. A necessary and sufficient condition for them to be bounded from a Banach function space into a weighted BMO is given, and their compactness in some particular cases is studied. Meanwhile, the embedding properties concerning the weighted BMO are investigated.

**[1]**C. Bennet and R. Sharpley,*Interpolation of operators*, Academic Press, New York, 1988. MR**928802 (89e:46001)****[2]**S. Bloom and R. Kerman,*Weighted norm inequalities for operators of Hardy type*, Proc. Amer. Math. Soc.**113**(1991), 135-141. MR**1059623 (91k:26018)****[3]**D. E. Edmunds, W. D. Evans, and D. J. Harris,*Approximation numbers of certain Volterra integral operators*, J. London Math. Soc. (2)**37**(1988), 471-489. MR**939123 (89k:47078)****[4]**Lai Qinsheng and L. Pick,*The Hardy operator*, ,*and*, J. London Math. Soc. (2) (to appear). MR**1223901 (94e:47042)****[5]**F. Martin-Reyes and E. Sawyer,*Weighted norm inequalities for the Riemann-Liouville fractional integral operators of order one and greater*, Proc. Amer. Math. Soc.**106**(1989), 727-733. MR**965246 (90a:26012)****[6]**B. Muckenhoupt and R. L. Wheeden,*Weighted bounded mean oscillation and the Hilbert transform*, Studia Math.**54**(1976), 221-237. MR**0399741 (53:3583)****[7]**B. Opic and A. Kufner,*Hardy-type inequalities*, Longman, Harlow, 1990. MR**1069756 (92b:26028)****[8]**U. Neri,*Some properties of functions with bounded mean oscillation*, Studia Math.**61**(1977), 63-75. MR**0445210 (56:3554)****[9]**V. D. Stepanov,*Two-weighted estimates for Riemann-Liouville integrals*, Ceskoslovenska Akad. Vld.**39**(1988), 1-28.**[10]**-,*Weighted inequalities for a class of Volterra convolution operators*, J. London Math. Soc. (2) (to appear). MR**1171551 (93f:47029)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1169887-9

Article copyright:
© Copyright 1994
American Mathematical Society