Singular integral operators, a brief historical overview of its evolution


  • Alejandro Ortiz Fernández Pontificia Universidad Católica del Perú



Operators, transforms, kernel, integral, Cauchy, weighs


In this work we give an analytical-historical view of the classical theory of singular integrals introduced by   A.P. Calderón-A. Zygmund. Emphasis is given to their applications to PDEs and to some projections of the  theory.


Benedek A, Calderón AP, Panzone R. Convolution Operators on Banach Space Valued Functions. Proc. Nat. Ac. Sci. USA. 1962; 356- 365.

Calderón AP. Intermediate Spaces and Interpolation. The Complex Method. Studia Math. 1964; 24:113.

Calderón AP. Uniqueness in the Cauchy problem of partial differential equations. Am. J. Math. 1958; 80:16-36.

Calderón AP. Existence and Uniqueness Theorems for Systems of Partial Differential Equations. Symp. Fluid Dyn. U. Marylands. Md. 1961.

Calderón AP. A Priori Estimates for Singular Integral Operators. C.I.M.E. Conf. Stresa. 1968.

Calderón AP, Zygmund A. On the Existence of Certain Singular Integrals. Acta Math. 1952; 88:85-139.

Calderón AP, Zygmund A. Singular Integrals and Periodic Functions. Studia Math. 1954; 14:249-271.

Calderón AP, Zygmund A. On Singular Integrals. Am. J. Math. 1956; 78:289-309.

Calderón AP, Zygmund A. Algebras of Certain Singular Integral Operators. Amer. J. Math. 1956; 78:310-320.

Calderón AP, Zygmund A. Singular Integral Operators and Differential Equations. Amer. J. Math. 1957; 74:901-921.

Calderón AP, Zygmund A. Local properties of solutions of elliptic partial differential equations. Studia Math.1961; 20:171-225.

Hörmander L. Pseudo-Differential Operators. Comm. Pure Appl. Math. 1965; 18:501-517.

Hörmander L. Pseudo-Differential Operator and Hypoelliptic Equations. Proc. Sym. on Singular Integrals. A.M.S. 1968.

Hörmander L. The Analysis of Linear Partial Differential Operators. 2da edition, Sweden: Springer Verlag.1990.

Kohn JJ, Nirenberg L. An Algebra of Pseudo-Differential Operators. Comm. Pure Appl. Math. 1965; 18:269-305.

Neri U. Singular Integrals. Springer-Verlag. 200, 1971.

Ortiz A. Operadores Integrales Singulares. Dpto. Mat. Univ. Nac. Trujillo. Perú. 1972.

Ortiz A. Algunos aspectos históricos-analíticos del análisis funcional. Selecciones Matemá́ticas. 2021; 8(2):386-40.

Ortiz A. Integrales Singulares. La Escuela de Chicago. Sec. Mat. PUCP. (virtual). Lima. 2011.

Ortiz A. Integrales Singulares y temas Afines. Pro Math. PUCP. 1991; V:9-10.

Ortiz A. Tópicos sobre Análisis Armónico. Notas de Mat. 4. Dpto. Mat. UNT. 1988.

Seeley RT. Singular integrals on compact manifolds. Amer. J. Math. 1959; 81:658-690.

Strömberg J-O, Torchinsky A. Weighted Hardy Spaces. Lect. Notes in Math.1381.Springer-Verlag.1989.

Torchinsky A. Singular Integrals in the Spaces A(B,X). Studia Math. 1973; 47.

Torchinsky A. Real-Variable Methods in Harmonic Analysis. Academic Press, INC. 1986, 462p.



How to Cite

Ortiz Fernández, A. . (2022). Singular integral operators, a brief historical overview of its evolution. Selecciones Matemáticas, 9(01), 01 - 23.