Skip to main content

Advertisement

SpringerLink
Log in

A Characterization of Two-Weight Trace Inequalities for Positive Dyadic Operators in the Upper Triangle Case

  • Published:
Potential Analysis Aims and scope Submit manuscript

Abstract

Two-weight trace inequalities for positive dyadic operators are characterized in terms of discrete Wolff’s potentials in the upper triangle case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cascante, C., Ortega, J.: On the boundedness of discrete Wolff potentials. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 8(2), 309–331 (2009)

    MATH  MathSciNet  Google Scholar 

  2. Cascante, C., Ortega, J., Verbitsky, I.: Nonlinear potentials and two-weight trace inequalities for general dyadic and radial kernels. Indiana Univ. Math. J. 53(3), 845–882 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cascante, C., Ortega, J., Verbitsky, I.: On L p-L q trace inequalities. J. Lond. Math. Soc. (2), 74(2), 497–511 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cascante, C., Ortega, J., Verbitsky, I.: Wolff’s inequality for radially nonincreasing kernels and applications to trace inequalities. Potential Anal. 16(4), 347–372 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

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

  7. Lacey, M., Sawyer, E., Shen, C.-Y., Uriarte-Tuero, I.: Two weight inequality for the Hilbert transform: a real variable characterization. arXiv:1201.4319 (2012)

  8. Lerner, A.: On an estimate of Calderón–Zygmund operators by dyadic positive operators. arXiv:1202.1860 (2012)

  9. Nazarov, F., Treil, S., Volberg, A.: The Bellman functions and two-weight inequalities for Haar multipliers. J. Am. Math. Soc. 12(4), 909–928 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  11. Sawyer, E.: A characterization of two-weight norm inequalities for fractional and Poisson integrals. Trans. Am. Math. Soc. 308(2), 533–545 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tanaka, H.: Two-weight norm inequalities for potential type integral operators in the case p > q > 0 and p > 1. Stud. Math. 216(1), 1–15 (2013)

    Article  MATH  Google Scholar 

  13. Tanaka, H., Gunawan, H.: The local trace inequality for potential type integral operators. Potential Anal. 38(2), 653–681 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  14. Tanaka, H., Terasawa Y.: Positive operators and maximal operators in a filtered measure space. J. Funct. Anal. 264(4), 920–946 (2013)

    Article  MATH  MathSciNet  Google Scholar 

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

Download references

Author information

Authors and Affiliations

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

    Hitoshi Tanaka

Authors
  1. Hitoshi Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hitoshi Tanaka.

Additional information

The author is supported by the FMSP program at Graduate School of Mathematical Sciences, the University of Tokyo, and Grant-in-Aid for Scientific Research (C) (No. 23540187), the Japan Society for the Promotion of Science.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tanaka, H. A Characterization of Two-Weight Trace Inequalities for Positive Dyadic Operators in the Upper Triangle Case. Potential Anal 41, 487–499 (2014). https://doi.org/10.1007/s11118-013-9379-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11118-013-9379-0

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation