Download Fourier Integrals in Classical Analysis (Cambridge Tracts in by Christopher D. Sogge PDF

By Christopher D. Sogge

This complicated monograph is worried with smooth remedies of significant difficulties in harmonic research. the most topic of the booklet is the interaction among principles used to review the propagation of singularities for the wave equation and their opposite numbers in classical research. particularly, the writer makes use of microlocal research to check difficulties related to maximal services and Riesz skill utilizing the so-called half-wave operator. to maintain the therapy self-contained, the writer starts with a fast overview of Fourier research and likewise develops the mandatory instruments from microlocal research. This moment version contains new chapters. the 1st offers Hörmander's propagation of singularities theorem and makes use of this to turn out the Duistermaat–Guillemin theorem. the second one issues more moderen effects with regards to the Kakeya conjecture, together with the maximal Kakeya estimates acquired via Bourgain and Wolff.

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