Singular integral operators, a brief historical overview of its evolution
DOI:
https://doi.org/10.17268/sel.mat.2022.01.01Keywords:
Operators, transforms, kernel, integral, Cauchy, weighsAbstract
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.
References
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Selecciones Matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.