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Singular integrals, spaces with fractional derivatives, characterization of Sobolev function by Bessel potentials,
capacity
Last update: T_KMA (02.05.2013)
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The course is completed by an oral exam. The required knowledge corresponds to the material delivered during the lectures. Last update: Malý Jan, prof. RNDr., DrSc. (10.05.2018)
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E. M. Stein: Singular integrals and differentiability properties of functions. Princeton University Press, Princeton, N.J. 1970 W. P. Ziemer: Weakly differentiable functions. Sobolev spaces and functions of bounded variation. Springer-Verlag, New York, 1989 Last update: T_KMA (02.05.2013)
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Singular integrals Calderon-Zygmund kernels L^2 estimate weak type L^1 estimate Marcinkiewicz interpolation theorem - special case Bessel and Riesz kernels Sobolev spaces of fractional order Characterization of Sobolev spaces in terms of Bessel potentials Hilbert and Riesz transform Poisson integral Energies and potentials Capacity Last update: Malý Jan, prof. RNDr., DrSc. (10.05.2018)
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Measure theory, Lebesgue integration, Fourier transform, distributions
Last update: Malý Jan, prof. RNDr., DrSc. (10.05.2018)
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