The collaboration begun by Zygmund and Calder�n in 1948 reached fruition in the Calder�n-Zygmund Theory of Singular Integrals and lasted more than three decades.
12.
This is well known in applications as ( essentially ) the Hilbert transform; it is also a basic example in mathematical analysis, in connection with singular integral operators.
13.
A synthesis of the theories of singular integrals and Mikhlin's multiplier theorem is widely used in different branches of mathematical analysis, particularly to the theory of differential equations.
14.
He also created the " H ?, ?, ? " function space and proved some theorems for nonlinear singular integral equations with Cauchy kernel within that space.
15.
A major result that uses the " L p, w "-spaces is the Marcinkiewicz interpolation theorem, which has broad applications to harmonic analysis and the study of singular integrals.
16.
Fefferman's work on partial differential equations, Fourier analysis, in particular convergence, multipliers, divergence, singular integrals and Hardy spaces earned him a Fields Medal at the International Congress of Mathematicians at Helsinki in 1978.
17.
In Moscow State University Evgeny Moiseev delivers the following lecture courses : Functional Analysis, Mathematical Analysis, Applied Functional Analysis, Mixed Equations, Singular Integral Equations, and Spectral Methods for Non-Classical Mathematical Physics Problems Solution.
18.
Calder�n s work, characterized by great originality, elegance and power reshaped the landscape of mathematical analysis and ranged over a wide variety of topics : from singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection.
19.
If " f " is a holomorphic univalent map from the unit disk " D " onto ? then the Bergman space of ? and its conjugate can be identified with that of " D " and " T " ? becomes the singular integral operator with kernel
20.
The " T " ( " b " ) theorem provides sufficient conditions for a singular integral operator to be a Calder�n & ndash; Zygmund operator, that is for a singular integral operator associated to a Calder�n & ndash; Zygmund kernel to be bounded on " L " 2.
