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A characterization for the boundedness of positive operators in a filtered measure space

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Abstract

In terms of a Sawyer type checking condition, a necessary and sufficient condition is obtained under which the positive operator in a filtered measure space is bounded from L p(d μ) to L q(dμ) with 1 < p ≤ q < ∞.

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References

  1. T. Hytönen, The A 2 theorem: remarks and complements, arXiv:1212.3840 (2012).

  2. M. Lacey, Two weight inequality for the Hilbert transform: a real variable characterization, II arXiv math:1301.4663 (2013).

  3. M. Lacey et al. Two weight inequality for the Hilbert transform: a real variable characterization, I, arXiv math:1201.4319 (2012).

  4. M. Lacey, E. Sawyer, and I. Uriarte-Tuero, Two weight inequalities for discrete positive operators, arXiv:0911.3437 (2009).

  5. E. Nakai and G. Sadasue, Martingale Morrey-Campanato spaces and fractional integrals, J. Funct. Spaces Appl. (2012), Article ID 673929, 29 pages.

  6. Nazarov F., Treil S., Volberg A.: The Bellman functions and two-weight inequalities for Haar multipliers. J. of Amer. Math. Soc. 12, 909–928 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sawano Y., Sugano S., Tanaka H.: Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces. Trans. Amer. Math. Soc. 363, 6481–6503 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Sawyer E.: A characterization of a two-weight norm inequality for maximal operators. Studia Math. 75, 1–11 (1982)

    MathSciNet  MATH  Google Scholar 

  9. Sawyer E.: A characterization of two weight norm inequalities for fractional and Poisson integrals. Trans. Amer. Math. Soc. 308, 533–545 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tanaka H., Terasawa Y.: Positive operators and maximal operators in a filtered measure space. J. Funct. Anal. 264, 920–946 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Treil, A remark on two weight estimates for positive dyadic operators, arXiv:1201.1455 (2012).

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, 153-8914, Japan

    Hitoshi Tanaka & Yutaka Terasawa

Authors
  1. Hitoshi Tanaka
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  2. Yutaka Terasawa
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Corresponding author

Correspondence to Yutaka Terasawa.

Additional information

H. Tanaka is supported by the Global COE program at Graduate School of Mathematical Sciences, the University of Tokyo, Grant-in-Aid for Scientific Research (C) (No. 23540187), the Japan Society for the Promotion of Science, and was supported by Fūjyukai foundation.

Y. Terasawa is a Research Fellow of the Japan Society for the Promotion of Science.

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Tanaka, H., Terasawa, Y. A characterization for the boundedness of positive operators in a filtered measure space. Arch. Math. 101, 559–568 (2013). https://doi.org/10.1007/s00013-013-0585-1

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  • DOI: https://doi.org/10.1007/s00013-013-0585-1

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