Abstract
That geometric considerations enter in a decisive way in many questions of harmonic analysis is by now a well-known fact. In explicit form such ideas arose first in the estimation of the Fourier transform of surface-carried measure; they have since played a key role in averages over lower-dimensional varieties, restriction theorems, in connection with the study of oscillatory integrals and Fourier integral operators, and in application to linear and non-linear dispersive equations.
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Stein, E.M. (2010). Some Geometrical Concepts Arising in Harmonic Analysis. In: Alon, N., Bourgain, J., Connes, A., Gromov, M., Milman, V. (eds) Visions in Mathematics. Modern Birkhäuser Classics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0422-2_17
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