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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weighted norm inequalities for general operators on monotone functions

Author: Shanzhong Lai
Journal: Trans. Amer. Math. Soc. 340 (1993), 811-836
MSC: Primary 42B10; Secondary 42B25, 47B38, 47G10
MathSciNet review: 1132877
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Abstract: In this paper we characterize the weights $ w,v$ for which $ {\left\Vert {{S_\phi }f} \right\Vert _{p,w}} \leq C{\left\Vert f \right\Vert _{q,v}}$, for $ f$ nonincreasing, where $ {S_\phi }f = \smallint _0^\infty {\phi (x,y)f(y)dy} $.

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  • [1] M. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for non-increasing functions, Trans. Amer. Math. Soc. 320 (1990), 727-735. MR 989570 (90k:42034)
  • [2] C. Bennett and R. Sharpley, Interpolation of operators, Math. 129, Academic Press, 1988. MR 928802 (89e:46001)
  • [3] M. Sh. Braverman, On a class of operators, preprint. MR 1200982 (94a:47052)
  • [4] H. P. Heinig, Weighted inequalities in Fourier analysis, preprint. MR 1151431 (93b:42015)
  • [5] M. A. Leckband and C. J. Neugebauer, A general maximal operator and the $ {A_p}$-condition, Trans. Amer. Math. Soc. 275 (1983), 821-831. MR 682735 (84c:42029)
  • [6] C. J. Neugebauer, Weighted norm inequalities for averaging operators of monotone functions, Publ. Mat. (to appear). MR 1201565 (93m:26042)
  • [7] C. J. Neugebauer, Some classical operators on Lorentz spaces, Forum Mat. (to appear). MR 1155311 (93i:42013)
  • [8] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158. MR 1052631 (91d:26026)
  • [9] D. Stepanov, The weighted Hardy's inequality for nonincreasing operators of monotone functions, preprint.

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Keywords: Weighted inequalities, strong type inequality, general operator
Article copyright: © Copyright 1993 American Mathematical Society

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