By Christopher D. Sogge
This complicated monograph is worried with glossy remedies of valuable difficulties in harmonic research. the most subject of the publication is the interaction among rules used to review the propagation of singularities for the wave equation and their opposite numbers in classical research. specifically, the writer makes use of microlocal research to check difficulties regarding maximal capabilities and Riesz capacity utilizing the so-called half-wave operator. to maintain the remedy self-contained, the writer starts off with a swift evaluation of Fourier research and in addition develops the required instruments from microlocal research. This moment variation comprises new chapters. the 1st provides Hörmander's propagation of singularities theorem and makes use of this to end up the Duistermaat-Guillemin theorem. the second one matters more moderen effects relating to the Kakeya conjecture, together with the maximal Kakeya estimates acquired by means of Bourgain and Wolff.
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