DOI QR코드

DOI QR Code

WEIGHTED INEQUALITIES FOR COMMUTATORS OF POTENTIAL TYPE OPERATORS

  • Li, Wenming
  • Published : 2007.11.30

Abstract

We derive a kind of weighted norm inequalities which relate the commutators of potential type operators to the corresponding maximal operators.

Keywords

weighted norm inequality;commutator;fractional integra;maximal function

References

  1. C. Bennett and R. Sharpley, Interpolation of operators Pure and Applied Mathematics, 129. Academic Press, Inc., Boston, MA, 1988
  2. Y. Ding, S. Z. Lu, and P. Zhang, Weak estimates for commutators of fractional integral operators, Sci. China Ser. A 44 (2001), no. 7, 877-888 https://doi.org/10.1007/BF02880137
  3. R. O'Neil, Fractional integration in Orlicz spaces. I., Trans. Amer. Math. Soc. 115 (1965), 300-328 https://doi.org/10.2307/1994271
  4. C. Perez, Sharp $L^p-weighted$ Sobolev inequalities, Ann. Inst. Fourier (Grenoble) 45 (1995), no. 3, 809-824 https://doi.org/10.5802/aif.1475
  5. C. Perez, Two weighted inequalities for potential and fractional type maximal operators, Indiana Univ. Math. J. 43 (1994), no. 2, 663-683 https://doi.org/10.1512/iumj.1994.43.43028
  6. C. Perez, On suffcient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted Lp-spaces with different weights, Proc. London Math. Soc. (3) 71 (1995), no. 1, 135-157 https://doi.org/10.1112/plms/s3-71.1.135
  7. C. Perez and R. L. Wheeden, Potential operators, maximal functions, and generalizations of $A\infty$, Potential Anal. 19 (2003), no. 1, 1-33 https://doi.org/10.1023/A:1022449810008
  8. E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Eu- clidean and homogeneous spaces, Amer. J. Math. 114 (1992), no. 4, 813-874 https://doi.org/10.2307/2374799

Cited by

  1. Weighted Inequalities for Multilinear Potential Operators and their Commutators vol.35, pp.3, 2011, https://doi.org/10.1007/s11118-010-9211-z
  2. The Local Trace Inequality for Potential Type Integral Operators vol.38, pp.2, 2013, https://doi.org/10.1007/s11118-012-9291-z
  3. MORREY SPACES AND FRACTIONAL OPERATORS vol.88, pp.02, 2010, https://doi.org/10.1017/S1446788709000457
  4. Potential operators and their commutators acting between variable Lebesgue spaces with different weights vol.29, pp.11, 2018, https://doi.org/10.1080/10652469.2018.1519807