Abstract
It is well known that the commutator T b of the singular integral operator T with a BMO function b is bounded on L p(R n), 1 < p < ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO–type estimate for T b is obtained under the assumption b ∈ LMO.
Similar content being viewed by others
References
Coifman, R. R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. of Math., 103, 611–635 (1976)
Chang, D. C. and Li, S. Y.: On the boundedness of multipliers, commutators and the second derivatives of Green’s operators on H 1 and BMO. Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28(4), 341–356 (1999)
Harbour, E., Segovia, C., Torrea, J. L.: Boundedness of commutators of fractional and singular integrals for the extreme values of p. Ill. J. Math., 41(4), 676–700 (1997)
Pèrez, C.: Endpoint estimates for commutators of singular integral operators. J. Func. Anal., 128(1), 163–185 (1995)
Stegenga, D. A.: Bounded Toeplitz operators on H 1 and applications of duality between H 1 and functions of bounded mean oscillation. Amer. J. Math., 98(3), 573–589 (1976)
Li, S. Y.: Applications of the singular integral operators in real and complex analysis. Adv. in Math. (Chinese), 29(3), 193–213 (2000)
John, F., Nirenberg, L.: On functions of bounded mean oscillation. Comm. Pure. Appl. Math., 14, 415–426 (1961)
Journé, J. L.: Calderón–Zygmund operators, Pseudo–Differential operators and the Cauchy integral of Calderón, Lecture Notes in Mathematics, 994, Springer–Verlag, Berlin, Heidelberg, 1983
Fefferman, C. L., Stein, E. M.: H p–spaces of several variables. Acta Math., 129, 137–193 (1972)
Spanne, S.: Some function spaces defined using the mean oscillation over cubes. Ann. Scuola Norm. Sup. Pisa., 19, 593–608 (1965)
Acquistapace, P.: On BMO regularity for linear elliptic systems. Ann. Mat. Pura Appl., 161(4), 231–269 (1992)
Nakai, E., Yabuta, K.: Pointwise multipliers for functions of bounded mean oscillation. J. Math. Soc. Japan, 37(2), 207–218 (1985)
Calderón, A. P., Zygmund, A.: On the existence of certain singular integrals. Acta Math., 88 85–139 (1952)
Stein, E. M.: Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by NSFC 10041005, 10171045
Rights and permissions
About this article
Cite this article
Sun, Y.Z., Su, W.Y. An Endpoint Estimate for the Commutator of Singular Integrals. Acta Math Sinica 21, 1249–1258 (2005). https://doi.org/10.1007/s10114-004-0468-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-004-0468-2