PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1994 | 109 | 2 | 105-131
Tytuł artykułu

On certain nonstandard Calderón-Zygmund operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in $ℝ^n$ related to the first Calderón commutator, but with a kernel which is far less regular.
Słowa kluczowe
Czasopismo
Rocznik
Tom
109
Numer
2
Strony
105-131
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-01-25
poprawiono
1993-08-17
Twórcy
Bibliografia
  • [BC] B. Bajsanski and R. Coifman, On singular integrals, in: Proc. Sympos. Pure Math. 10, Amer. Math. Soc., Providence, 1967, 1-17.
  • [Ca] A. P. Calderón, Commutators of singular integrals, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092-1099.
  • [CZ] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289-309.
  • [CC] C. P. Calderón, On commutators of singular integrals, Studia Math. 53 (1975), 139-174.
  • [CS] A. Carbery and A. Seeger, Conditionally convergent series of linear operators on $L^p$-spaces and $L^p$-estimates for pseudodifferential operators, Proc. London Math. Soc. 57 (1988), 481-510.
  • [C] M. Christ, Weak type (1,1) bounds for rough operators, Ann. of Math. 128 (1988), 19-42.
  • [C2] M. Christ, Hilbert transforms along curves I. Nilpotent groups, ibid. 122 (1985), 575-596.
  • [Co] J. Cohen, A sharp estimate for a multilinear singular integral in $ℝ^n$, Indiana Univ. Math. J. 30 (1981), 693-702.
  • [CDMS] R. Coifman, G. David, Y. Meyer and S. Semmes, ω-Calderón-Zygmund operators, in: Proc. Conf. Harmonic Analysis and PDE, El Escorial 1987, Lecture Notes in Math. 1384, Springer, Berlin, 1989, 132-145.
  • [CRW] R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635.
  • [DJ] G. David and J.-L. Journé, A boundedness criterion for generalized Calderón-Zygmund operators, ibid. 120 (1984), 371-397.
  • [DJS] G. David, J.-L. Journé and S. Semmes, Calderón-Zygmund operators, para-accretive functions and interpolation, preprint.
  • [DR] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561.
  • [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985.
  • [HH] Y. S. Han and S. Hofmann, T1 theorems for Besov and Triebel-Lizorkin spaces, Trans. Amer. Math. Soc., to appear.
  • [HS] Y. S. Han and E. T. Sawyer, Para-accretive functions, the weak boundedness property, and interpolation, Rev. Mat. Iberoamericana, to appear.
  • [H] S. Hofmann, Weighted inequalities for commutators of rough singular integrals, Indiana Univ. Math. J. 39 (1990), 1275-1304.
  • [H2] S. Hofmann, Singular integrals of Calderón-type in $ℝ^n$, and BMO, Rev. Mat. Iberoamericana, to appear.
  • [Hu] Y. Hu, An estimate for multilinear singular integrals on $ℝ^n$, Beijing Daxue Xuebao 1985 (3), 19-26 (in Chinese, with English summary reprinted in MR 87h:42026).
  • [J] J.-L. Journé, Calderón-Zygmund Operators, Pseudo-Differential Operators, and the Cauchy Integral of Calderón, Lecture Notes in Math. 994, Springer, Berlin, 1983.
  • [M] Y. Meyer, La continuité des opérateurs définis par des intégrales singulières, Monografías de Matemáticas V. 4, Univ. Autónoma de Madrid.
  • [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv109i2p105bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.