@article{2752,
abstract = {We prove L p -bounds on the Fourier transform of measures μ supported on two dimensional surfaces. Our method allows to consider surfaces whose Gauss curvature vanishes on a one-dimensional submanifold. Under a certain non-degeneracy condition, we prove that μ ∧ ε L 4+β, β > 0, and we give a logarithmically divergent bound on the L 4-norm. We use this latter bound to estimate almost singular integrals involving the dispersion relation, e(p)= ∑13 [1-\cos p_j]} , of the discrete Laplace operator on the cubic lattice. We briefly explain our motivation for this bound originating in the theory of random Schrödinger operators.},
author = {László Erdös and Salmhofer, Manfred},
journal = {Mathematische Zeitschrift},
number = {2},
pages = {261 -- 294},
publisher = {Springer},
title = {{Decay of the Fourier transform of surfaces with vanishing curvature}},
doi = {10.1007/s00209-007-0125-4},
volume = {257},
year = {2007},
}