Open AccessOscillatory singular integrals and harmonic analysis on nilpotent groups
Author(s) -
Fulvio Ricci,
Elias M. Stein
Publication year - 1986
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.83.1.1
Subject(s) - nilpotent , mathematics , automorphism , pure mathematics , context (archaeology) , exponential function , harmonic , lie group , lie algebra , singular integral , algebra over a field , mathematical analysis , physics , integral equation , quantum mechanics , paleontology , biology
Several related classes of operators on nilpotent Lie groups are considered. These operators involve the following features: (i ) oscillatory factors that are exponentials of imaginary polynomials, (ii ) convolutions with singular kernels supported on lower-dimensional submanifolds, (iii ) validity in the general context not requiring the existence of dilations that are automorphisms.