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Boundedness for Marcinkiewicz integrals associated with Schrödinger operators

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Abstract

Let L = −Δ + V be a Schrödinger operator, where Δ is the Laplacian on \(\mathbb {R}^{n}\), while nonnegative potential V belongs to the reverse Hölder class. In this paper, we will show that Marcinkiewicz integral associated with Schrödinger operator is bounded on BMO L , and from \(H^{1}_{L}(\mathbb {R}^{n})\) to \(L^{1}(\mathbb {R}^{n})\).

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References

  1. Benedek A, Calderón A P and Panzone R, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962) 356–365

    Article  MATH  MathSciNet  Google Scholar 

  2. Ding Y, Lu S and Xue Q, Marcinkiewicz integral on Hardy spaces, Integr. Equ. Oper. Theory. 42 (2002) 174–182

    Article  MATH  MathSciNet  Google Scholar 

  3. Dong J and Liu H, The BMOL space and Riesz transforms associated with Schrödinger operators, Acta Math. Sin. (Engl. Ser.) 26 (2010) 659–668

    Article  MATH  MathSciNet  Google Scholar 

  4. Dziuba´nski J and Zienkiewicz J, Hardy space H 1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality, Rev. Mat. Iber. 15 (1999) 279–296

    Article  MATH  Google Scholar 

  5. Dziuba´nski J, Garrigós G, Torrea J and Zienkiewicz J, BMO spaces related to Shrödinger operators with potentials satisfying a reverse Hölder inequality, Math. Z. 249 (2005) 249–356

    Google Scholar 

  6. Fefferman C and Stein E, Hp-space of serval variables, Acta Math 46 (1972) 137–193

    Article  MathSciNet  Google Scholar 

  7. Shen Z, L p estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier. Grenoble 45 (1995) 513–546

    Article  MATH  MathSciNet  Google Scholar 

  8. Stein E, On the functions of Littlewood–Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958) 430–466

    Article  MathSciNet  Google Scholar 

  9. Torchinsky A and Wang S, A note on Marcinkiewicz integral, Colloq. Math. 47 (1990) 235–243

    MathSciNet  Google Scholar 

Download references

Acknowledgement

This research was supported by the NNSF (111271024) of China.

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Authors and Affiliations

  1. School of Applied Mathematics, Beijing Normal University Zhuhai, Zhuhai, 519085, People’s Republic of China

    WENHUA GAO

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    LIN TANG

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  1. WENHUA GAO
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  2. LIN TANG
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Correspondence to LIN TANG.

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GAO, W., TANG, L. Boundedness for Marcinkiewicz integrals associated with Schrödinger operators. Proc Math Sci 124, 193–203 (2014). https://doi.org/10.1007/s12044-014-0168-5

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  • DOI: https://doi.org/10.1007/s12044-014-0168-5

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