Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Linear monotone operators and weighted BMO

Author: Qinsheng Lai
Journal: Proc. Amer. Math. Soc. 120 (1994), 875-887
MSC: Primary 42B99; Secondary 47B38
MathSciNet review: 1169887
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [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, $ {L_\infty }$, and $ BMO$, 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42B99, 47B38

Retrieve articles in all journals with MSC: 42B99, 47B38

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society