Singular integrals
HTML articles powered by AMS MathViewer
- by A. P. Calderón PDF
- Bull. Amer. Math. Soc. 72 (1966), 427-465
References
-
1. A. Besicovitch, Sur la nature des fonctions a carré sommable mésurables, Fund. Math. 4 (1923), 172-195.
- A. Benedek, A.-P. Calderón, and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356–365. MR 133653, DOI 10.1073/pnas.48.3.356
- A.-P. Calderón, Commutators of singular integral operators, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092–1099. MR 177312, DOI 10.1073/pnas.53.5.1092
- A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 52553, DOI 10.1007/BF02392130
- A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289–309. MR 84633, DOI 10.2307/2372517
- A. P. Calderón and A. Zygmund, Singular integrals and periodic functions, Studia Math. 14 (1954), 249–271 (1955). MR 69310, DOI 10.4064/sm-14-2-249-271
- Lars Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93–140. MR 121655, DOI 10.1007/BF02547187
- J. Horváth, Sur les fonctions conjuguées à plusieurs variables, Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15 (1953), 17–29 (French). MR 0053276, DOI 10.1016/S1385-7258(53)50004-6 10. J. Marcinkiewicz, Sur quelques intégrales du type de Dini, Ann. Soc. Polon. Math. 17 (1938), 42-50.
- Lynn H. Loomis, A note on the Hilbert transform, Bull. Amer. Math. Soc. 52 (1946), 1082–1086. MR 19155, DOI 10.1090/S0002-9904-1946-08713-3 12. S. G. Mihlin, Multidimensional singular integrals and singular equations, Moscow 1962. (Russian)
- S. G. Mihlin, Singular integral equations, Amer. Math. Soc. Translation 1950 (1950), no. 24, 116. MR 0036434
- R. O’Neil and G. Weiss, The Hilbert transform and rearrangement of functions, Studia Math. 23 (1963), 189–198. MR 160084, DOI 10.4064/sm-23-2-189-198 15. A. Plessner, Zur Theorie der konjugierten trigonometrischen Reihen, Mitt. Math. Sem. Giessen 10 (1923), 1-36. 16. I. I. Privalov, Intégrale de Cauchy, Saratov (1919), 1-104. (Russian) 17. M. Riesz, Sur les fonctions conjuguées, Math. Z. 27 (1927), 218-244.
- J. Schwartz, A remark on inequalities of Calderon-Zygmund type for vector-valued functions, Comm. Pure Appl. Math. 14 (1961), 785–799. MR 143031, DOI 10.1002/cpa.3160140410
- E. M. Stein, On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430–466. MR 112932, DOI 10.1090/S0002-9947-1958-0112932-2
- E. M. Stein, Note on singular integrals, Proc. Amer. Math. Soc. 8 (1957), 250–254. MR 88606, DOI 10.1090/S0002-9939-1957-0088606-8
- E. M. Stein and Guido Weiss, An extension of a theorem of Marcinkiewicz and some of its applications, J. Math. Mech. 8 (1959), 263–284. MR 0107163, DOI 10.1512/iumj.1959.8.58019 22. F. G. Tricomi, Formula d’inversione dell’ordine di due integrazioni doppie "con asterisco," Rend. Accad. Naz. Lincei 3 (1926), 535-539.
- Mary Weiss and A. Zygmund, An example in the theory of singular integrals, Studia Math. 26 (1965), 101–111. MR 190655, DOI 10.4064/sm-26-1-101-111
- A. Zygmund, On singular integrals, Rend. Mat. e Appl. (5) 16 (1957), 468–505. MR 96088 25. A. Zygmund, Trigonometric series. I, II, Cambridge Univ. Press, Cambridge, 1959.
- S. G. Mihlin, On the multipliers of Fourier integrals, Dokl. Akad. Nauk SSSR (N.S.) 109 (1956), 701–703 (Russian). MR 0080799 27. J. Marcinkiewicz, Sur les multiplicateurs des séries de Fourier, Studia Math. 8 (1939), 78-91. 28. S. Vagi, On multipliers and singular integrals for vector valued functions, Doctoral Dissertation, Univ. of Chicago, Chicago, Ill., 1965.
- Mischa Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105–167 (1956) (English, with Spanish summary). MR 84632
- Giuseppe Arnese, Maggiorazioni in $L^{p}$ die potenziali relativi all’equazione del calore, Ricerche Mat. 13 (1964), 147–191 (Italian). MR 197953 31. E. Fabes, Parabolic partial differential equations and singular integral operators, Doctoral Dissertation, Univ. of Chicago, Chicago, Ill., 1965. 32. E. Fabes and N. Riviere, Singular integral operators with mixed homogeneity, Studia Math. (to appear)
- E. B. Fabes and C. Sadosky, Pointwise convergence for parabolic singular integrals, Studia Math. 26 (1966), 225–232. MR 209786, DOI 10.4064/sm-26-3-225-232
- B. Frank Jones Jr., A class of singular integrals, Amer. J. Math. 86 (1964), 441–462. MR 161099, DOI 10.2307/2373175
- Cora Sadosky, On some properties of a class of singular integrals, Studia Math. 27 (1966), 73–86. MR 203410, DOI 10.4064/sm-27-1-73-86
- A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901–921. MR 100768, DOI 10.2307/2372441
- A. P. Calderón and A. Zygmund, On a problem of Mihlin, Trans. Amer. Math. Soc. 78 (1955), 209–224. MR 68028, DOI 10.1090/S0002-9947-1955-0068028-9
- Georges Giraud, Équations à intégrales principales; étude suivie d’une application, Ann. Sci. École Norm. Sup. (3) 51 (1934), 251–372 (French). MR 1509344, DOI 10.24033/asens.842 39. G. Giraud, Sur une classe générale d’équations à intégrales principales, C. R. Acad. Sci. Paris 202 (1936), 2124-2126.
- A. S. Dynin, Singular operators of arbitrary order on a manifold, Dokl. Akad. Nauk SSSR 141 (1961), 21–23 (Russian). MR 0155205
- I. C. Gohberg, On the theory of multidimensional singular integral equations, Soviet Math. Dokl. 1 (1960), 960–963. MR 0124704
- J. J. Kohn, Singular integral equations for differential forms on Riemannian manifolds, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 650–653. MR 92095, DOI 10.1073/pnas.42.9.650
- J. J. Kohn and D. C. Spencer, Complex Neumann problems, Ann. of Math. (2) 66 (1957), 89–140. MR 87879, DOI 10.2307/1970119
- R. T. Seeley, Singular integrals on compact manifolds, Amer. J. Math. 81 (1959), 658–690. MR 110022, DOI 10.2307/2372921
- R. T. Seeley, Integro-differential operators on vector bundles, Trans. Amer. Math. Soc. 117 (1965), 167–204. MR 173174, DOI 10.1090/S0002-9947-1965-0173174-1
- Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI 10.1002/cpa.3160180307
- J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. MR 176362, DOI 10.1002/cpa.3160180121
- R. T. Seeley, Refinement of the functional calculus of Calderón and Zygmund, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 521–531. MR 0226450, DOI 10.1016/S1385-7258(65)50054-8
- André Unterberger and Juliane Bokobza, Les opérateurs de Calderon-Zygmund précisés, C. R. Acad. Sci. Paris 259 (1964), 1612–1614 (French). MR 176360
- André Unterberger and Juliane Bokobza, Sur une généralisation des opérateurs de Calderón-Zygmund et des espaces $H^{s}$, C. R. Acad. Sci. Paris 260 (1965), 3265–3267 (French). MR 188832
- A.-P. Calderón and A. Zygmund, Local properties of solutions of elliptic partial differential equations, Studia Math. 20 (1961), 171–225. MR 136849, DOI 10.4064/sm-20-2-181-225
- A.-P. Calderón and A. Zygmund, On the differentiability of functions which are of bounded variation in Tonelli’s sense, Rev. Un. Mat. Argentina 20 (1962), 102–121. MR 151557
- A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36. MR 104925, DOI 10.2307/2372819
- Alberto-P. Calderón, Integrales singulares y sus aplicaciones a ecuaciones diferenciales hiperbolicas, Universidad de Buenos Aires, Buenos Aires, 1960 (Spanish). Cursos y Seminarios de Matemática, Fasc. 3. MR 0123834
- A.-P. Calderón, Existence and uniqueness theorems for systems of partial differential equations, Fluid Dynamics and Applied Mathematics (Proc. Sympos., Univ. of Maryland, 1961) Gordon and Breach, New York, 1962, pp. 147–195. MR 0156078
- A.-P. Calderón, Boundary value problems for elliptic equations, Outlines Joint Sympos. Partial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp. 303–304. MR 0203254
- Irwin S. Bernstein, On the unique continuation problem of elliptic partial differential equations, J. Math. Mech. 10 (1961), 579–606. MR 0123086
- I. Norman Katz, On the existence of weak solutions to linear partial differential equations, J. Math. Anal. Appl. 2 (1961), 111–144. MR 151714, DOI 10.1016/0022-247X(61)90050-6
- K. O. Friedrichs and P. D. Lax, Boundary value problems for first order operators, Comm. Pure Appl. Math. 18 (1965), 355–388. MR 174999, DOI 10.1002/cpa.3160180127 60. J. Neuwirth, Totally hyperbolic partial differential equations, Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, Mass., 1959.
- Sigeru Mizohata, Note sur le traitement par les opérateurs d’intégrale singulière du problème de Cauchy, J. Math. Soc. Japan 11 (1959), 234–240 (French). MR 123836, DOI 10.2969/jmsj/01130234
- R. T. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781–809. MR 209915, DOI 10.2307/2373078
- M. F. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422–433. MR 157392, DOI 10.1090/S0002-9904-1963-10957-X
- R. T. Seeley, Regularization of singular integral operators on compact manifolds, Amer. J. Math. 83 (1961), 265–275. MR 123167, DOI 10.2307/2372955
- R. T. Seeley, The index of elliptic systems of singular integral operators, J. Math. Anal. Appl. 7 (1963), 289–309. MR 159247, DOI 10.1016/0022-247X(63)90054-4
- A. I. Vol′pert, The index of systems of two-dimensional singular integral equations. , Dokl. Akad. Nauk SSSR 142 (1962), 776–777 (Russian). MR 0132370
Additional Information
- Journal: Bull. Amer. Math. Soc. 72 (1966), 427-465
- DOI: https://doi.org/10.1090/S0002-9904-1966-11492-1
- MathSciNet review: 0209918