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Sharp Estimates for Multilinear Commutator of Littlewood-Paley Operator

Jinliang Hao|Lanzhe Liu
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회논문집 (Communications of the KMS)|제23권 제1호|pp. 49-59

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참고문헌

키워드

BMOmultilinear commutatorLittlewood-Paley operatorsharp inequality.
주제분류수학

초록

In this paper, we prove the sharp estimates for multilinearcommutator related to Littlewod-Paley operator. By using the sharp es-timates, we obtained the weighted Lp-norm inequality for the multilinearcommutator for 1< p < ∞.

Abstract

In this paper, we prove the sharp estimates for multilinearcommutator related to Littlewod-Paley operator. By using the sharp es-timates, we obtained the weighted Lp-norm inequality for the multilinearcommutator for 1< p < ∞.

참고문헌 (12)

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  2. R. Coifman, "Wavelets, Calder´on-Zygmund and Multilinear Operators, Cambridge Studies in Advanced Math", pp.48~ (1997), Cambridge University Press
  3. R. Coifman, "Factorization theorems for Hardy spaces in several variables", Ann. of Math, 103, pp.611~635 (1976)
  4. J. Garcia-Cuerva, "Weighted Norm Inequalities and Related Topics, North-Holland Math", pp.16~ (1985), Amsterdam
  5. G. Hu, "A variant sharp estimate for multilinear singular integral operators", Studia Math, 141, pp.25~42 (2000)
  6. L. Z. Liu, "Weighted weak type estimates for commutators of Littlewood-Paley operator", Japanese J. Math, 29(1), pp.1~13 (2003)
  7. L. Z. Liu, "The continuity of commutators on Triebel-Lizorkin spaces", Integral Equations and Operator Theory, 49(1), pp.65~76 (2004)
  8. C. P´erez, "Endpoint estimate for commutators of singular integral operators", J. Func. Anal, 128, pp.163~185 (1995)
  9. C. P´erez, "Sharp weighted endpoint estimates for commutators of singular integral operators", Michigan Math. J, 49, pp.23~37 (2001)
  10. C. P´erez, "Sharp weighted estimates for multilinear commutators", J. London Math. Soc, 65, pp.672~692 (2002)
  11. E. M. Stein, "Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals" (1993), Princeton Univ. Press
  12. A. Torchinsky, "The Real Variable Methods in Harmonic Analysis, Pure and Applied Math", pp.123~ (1986), Academic Press

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