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Endpoint estimates for multilinear fractional maximal operators

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We study the mapping property of multilinear fractional \linebreak 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.

Abstract

We study the mapping property of multilinear fractional \linebreak 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.

참고문헌 (9)

  1. S. M. Buckley, "Is the maximal function of a Lipschitz function continuous?", Ann. Acad. Sci. Fenn. Math, 24(2), pp.519~528 (1999)
  2. Zun-wei Fu, "Characterization for commutators of n-dimensional fractional Hardy operators", Science in China Series A: Mathematics, 50(10), pp.1418~1426 (2007), Springer Science and Business Media LLC[DOI]
  3. L. Grafakos, "Multilinear Calderon-Zygmund operators on Hardy spaces", Collect. Math, 52(2), pp.169~179 (2001)
  4. Loukas Grafakos, "Multilinear Calderón–Zygmund Theory", Advances in Mathematics, 165(1), pp.124~164 (2002), Elsevier BV[DOI]
  5. Loukas Grafakos, "Maximal operator and weighted norm inequalities for multilinear singular integrals", Indiana University Mathematics Journal, 51(5), pp.1261~1276 (2002), Indiana University Mathematics Journal[DOI]
  6. T. Heikkinen, "Fractional maximal functions in metric measure spaces", Anal. Geom. Metr. Spaces, 1, pp.147~162 (2013)
  7. Jaak Peetre, "On the theory of Lp,λ spaces", Journal of Functional Analysis, 4(1), pp.71~87 (1969), Elsevier BV[DOI]
  8. LIN TANG, "ENDPOINT ESTIMATES FOR MULTILINEAR FRACTIONAL INTEGRALS", Journal of the Australian Mathematical Society, 84(03), pp.419~429 (2008), Cambridge University Press (CUP)[DOI]
  9. J. Zhou, "Lipschitz spaces and fractional integral operators associated with nonhomogeneous metric measure spaces", Abstr. Appl. Anal, 2014 (2014)[DOI]

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