Harmonic functions in a domain U can be expressed in terms of averages of its values at the boundary of U. Such averages are expressed in integral operators. Understanding the behaviour of integral operators at the boundary points leads to the study of the most characteristic tools in Harmonic Analysis: maximal functions, singular integrals and oscillatory integrals. In this talk we discuss such operators, their motivation and relevance, as well as recent results on oscillatory integrals with strong singularities.
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