Singular integral operators of Calderón type and related operators on the energy spaces
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- by Takafumi Murai PDF
- Trans. Amer. Math. Soc. 288 (1985), 161-178 Request permission
Abstract:
We show the boundedness of some singular integral operators on the energy spaces.References
- Michael Beals and Michael Reed, Propagation of singularities for hyperbolic pseudodifferential operators with nonsmooth coefficients, Comm. Pure Appl. Math. 35 (1982), no. 2, 169–184. MR 644021, DOI 10.1002/cpa.3160350203
- Gérard Bourdaud, Une extension du théorème des commutateurs de Calderón, Seminar on Harmonic Analysis, 1981–1982, Publ. Math. Orsay 83, vol. 2, Univ. Paris XI, Orsay, 1983, pp. 36–47 (French). MR 710678
- A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
- Lennart Carleson, Selected problems on exceptional sets, Van Nostrand Mathematical Studies, No. 13, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0225986
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250 R. R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque 57 (1978).
- R. R. Coifman, G. David, and Y. Meyer, La solution des conjecture de Calderón, Adv. in Math. 48 (1983), no. 2, 144–148 (French). MR 700980, DOI 10.1016/0001-8708(83)90084-1
- R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
- N. S. Landkof, Foundations of modern potential theory, Die Grundlehren der mathematischen Wissenschaften, Band 180, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy. MR 0350027, DOI 10.1007/978-3-642-65183-0
- Takafumi Murai, Boundedness of singular integral operators of Calderón type, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 8, 364–367. MR 726524
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 288 (1985), 161-178
- MSC: Primary 42A50; Secondary 46E35, 47G05
- DOI: https://doi.org/10.1090/S0002-9947-1985-0773054-7
- MathSciNet review: 773054