Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ENDPOINT ESTIMATES FOR MULTILINEAR FRACTIONAL MAXIMAL OPERATORS

  • He, Suixin (College of Mathematics and Statistics Yili Normal University) ;
  • Zhang, Jing (College of Mathematics and Statistics Yili Normal University)
  • Received : 2019.03.12
  • Accepted : 2019.07.09
  • Published : 2020.03.31
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Abstract

We study the mapping property of multilinear fractional maximal operators in Lipschitz spaces. It should be pointed out that some of the techniques employed in the study of fractional integral operators do not apply to fractional maximal operators.

Keywords

References

  1. S. M. Buckley, Is the maximal function of a Lipschitz function continuous?, Ann. Acad. Sci. Fenn. Math. 24 (1999), no. 2, 519-528.
  2. Z. W. Fu, Z. G. Liu, S. Z. Lu, and H. B. Wang, Characterization for commutators of n-dimensional fractional Hardy operators, Sci. China Ser. A 50 (2007), no. 10, 1418-1426. https://doi.org/10.1007/s11425-007-0094-4
  3. L. Grafakos and N. Kalton, Multilinear Calderon-Zygmund operators on Hardy spaces, Collect. Math. 52 (2001), no. 2, 169-179.
  4. L. Grafakos and R. H. Torres, Multilinear Calderon-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124-164. https://doi.org/10.1006/aima.2001.2028
  5. L. Grafakos and R. H. Torres, Maximal operator and weighted norm inequalities for multilinear singular integrals, Indiana Univ. Math. J. 51 (2002), no. 5, 1261-1276. https://doi.org/10.1512/iumj.2002.51.2114
  6. T. Heikkinen, J. Lehrback, J. Nuutinen, and H. Tuominen, Fractional maximal functions in metric measure spaces, Anal. Geom. Metr. Spaces 1 (2013), 147-162. https://doi.org/10.2478/agms-2013-0002
  7. J. Peetre, On the theory $\mathcal{L}_{p},{\lambda}$ spaces, J. Functional Analysis 4 (1969), 71-87. https://doi.org/10.1016/0022-1236(69)90022-6
  8. L. Tang, Endpoint estimates for multilinear fractional integrals, J. Aust. Math. Soc. 84 (2008), no. 3, 419-429. https://doi.org/10.1017/S1446788708000724
  9. J. Zhou and D. Wang, Lipschitz spaces and fractional integral operators associated with nonhomogeneous metric measure spaces, Abstr. Appl. Anal. 2014 (2014), Art. ID 174010, 8 pp. https://doi.org/10.1155/2014/174010