# Alberto P. Calderon

Wolf Prize Laureate in Mathematics 1989

**Alberto P. Calderon**

#### Affiliation at the time of the award:

**University of Chicago, USA**

#### Award citation:

**“for his groundbreaking work on singular integral operators and their application to and important problems in partial differential equations”.**

#### Prize share:

**Alberto P. Calderon**

**John W. Milnor **

Alberto P. Calderon (born in 1920, Argentina) commenced his academic journey at the University of Buenos Aires, focusing on engineering studies. Upon completing his degree in civil engineering in 1947, Calderon secured a position within the research laboratory of the geophysical division at YPF (Yacimientos Petrolíferos Fiscales), a state-owned oil company in Argentina. His work at the YPF Lab centered on exploring methods to determine the conductivity of a body by conducting electrical measurements at its boundary. Although he didn’t publish his findings until 1980 in a brief Brazilian paper, Calderon’s research marked an essential contribution to the field.Subsequently, Calderon transitioned to a role at the University of Buenos Aires. In 1948, Antoni Zygmund from the University of Chicago arrived at the university following an invitation by Alberto González Domínguez. Calderon was then designated as Zygmund’s assistant. Impressed by Calderon’s potential, Zygmund extended an invitation for Calderon to collaborate with him. In 1949, Calderon relocated to Chicago with the support of a Rockefeller Fellowship. Under the guidance of Marshall Stone’s encouragement to pursue a doctorate, Calderon utilized three recently published papers as his dissertation and earned his PhD in mathematics under Zygmund’s supervision in 1950.

The work of Professor Alberto P. Calderon has had a lasting impact on the shape of contemporary Fourier analysis and on its connections with real variables, complex analysis, and partial differential equations. In particular, his contributions to the theory of singular integral operators (SIO) have been decisive, both through the introduction of the sharpest technical tools into that theory and through its imaginative application to important problems in partial differential equations.

Together with his teacher, Antoni Zygmund, Calderon proved the famous theorem on the LP boundedness (1<P<∞) of SIO and introduced the important Calderon-Zygmund decomposition. Subsequently, he used SIO to establish the first general result on the uniqueness of the Cauchy problem. for higher order partial differential operators and systems. He then applied this machinery to obtain general results on local solvability for linear partial differential equations (independently of, and contemporaneously with, Hormander) and also gave the first general method of reducing elliptic boundary value problems for equations on the boundary. These papers provided the major stimulus for the development of pseudodifferential operators. At about the same time, he introduced the complex method of interpolation of operators in general banach spaces (contemporaneously with, J.L. Lions). with his celebrated theorem on the first commutator, Calderon initiated a new and fruitful attack on the theory of SIO, which reached a culmination in his paper on the Cauchy integral on Lipschitz curves, honored by the Bocher Prize. In this work, Calderon not only settled an important problem of long-standing in complex function theory but also apened up new vistas for research in classical analysis.