--- res: bibo_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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: László foaf_name: László Erdös foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Manfred foaf_name: Salmhofer, Manfred foaf_surname: Salmhofer bibo_doi: 10.1007/s00209-007-0125-4 bibo_issue: '2' bibo_volume: 257 dct_date: 2007^xs_gYear dct_publisher: Springer@ dct_title: Decay of the Fourier transform of surfaces with vanishing curvature@ ...