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Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over ℝn

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Abstract

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces. The sharpness of some results is also investigated.

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References

  1. R R Coifman, Y Meyer. Au-delà des opéerateurs pseudo-différentiels. Paris: Astérisque, No 57, Soc Math France, 1978

  2. J García-Cuerva, K S Kazarian. Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces. Studia Math, 1994, 109(3): 255-276

    MATH  MathSciNet  Google Scholar 

  3. J García-Cuerva, Rubio de J L Francia. Weighted norm inequalities and related topics. Amsterdam: Notas de Math, No 116, North Holland, 1985

  4. J-L Journé. Calderón-Zygmund Operators, Pseudo-Differential Operators and the Cauchy Integral of Calderón. Berlin: Lecture Notes in Math, No 994, Springer-Verlag, 1983

  5. E M Stein. Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton: Princeton Univ Press, NJ, 1993

  6. K Yabuta. Generalizations of Calderón-Zygmund operators. Studia Math, 1985, 82: 17-31

    MATH  MathSciNet  Google Scholar 

  7. R Fefferman, F Soria. The space weak H 1. Studia Math, 1987, 85: 1-16

    MathSciNet  Google Scholar 

  8. H Liu. The weak H p spaces on homogeneous groups. Berlin: Lecture Notes in Math, No 1494, Springer-Verlag, 1991, 113-118

  9. Y Zhang. On Oscillatory Integral Operators (in Chinese). Beijing: PhD Thesis, Beijing Normal Univ, 1990

  10. J Alvarez. H p and weak H p continuity of Calderón-Zygmund type operators. Marcel Dekker: Fourier Analysis: Analytic and Geometric Aspects, 1994, 17-34

  11. S Lu, D Yang. Weak Hardy spaces over locally compact Vilenkin groups (in Chinese). J of Beijing Normal Univ (Natural Sci) 1992, 28: 409-419

    MATH  Google Scholar 

  12. T S Quek, D Yang. Weighted weak Hardy spaces on bounded locally compact Vilenkin groups. Preprint, 1998

  13. J O Strömberg , Torchinsky A. Weighted Hardy Spaces. Berlin: Lecture Notes in Math, No 1381, Springer-Verlag, 1989

  14. H Triebel. Theory of Function Spaces. Basel: Birkhäuser Verlag, 1983

  15. F Soria, G Weiss. A remark on singular integrals and power weights. Indiana Univ Math J, 1994, 43: 187-204

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Tongseng Quek.

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* Dachun Yang was partially supported by the NNSF and the SEDF of China

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Quek, T., Yang*, D. Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over ℝn . Acta Math Sinica 16, 141–160 (2000). https://doi.org/10.1007/s101149900022

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  • DOI: https://doi.org/10.1007/s101149900022

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