{"publication_status":"published","type":"journal_article","doi":"10.1007/s00209-007-0125-4","volume":257,"issue":"2","month":"01","publisher":"Springer","date_published":"2007-01-01T00:00:00Z","publication":"Mathematische Zeitschrift","author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"László Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Manfred","last_name":"Salmhofer","full_name":"Salmhofer, Manfred"}],"date_updated":"2021-01-12T06:59:28Z","page":"261 - 294","year":"2007","abstract":[{"text":"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 &gt; 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.","lang":"eng"}],"title":"Decay of the Fourier transform of surfaces with vanishing curvature","quality_controlled":0,"publist_id":"4140","day":"01","extern":1,"citation":{"ista":"Erdös L, Salmhofer M. 2007. Decay of the Fourier transform of surfaces with vanishing curvature. Mathematische Zeitschrift. 257(2), 261–294.","ama":"Erdös L, Salmhofer M. Decay of the Fourier transform of surfaces with vanishing curvature. <i>Mathematische Zeitschrift</i>. 2007;257(2):261-294. doi:<a href=\"https://doi.org/10.1007/s00209-007-0125-4\">10.1007/s00209-007-0125-4</a>","ieee":"L. Erdös and M. Salmhofer, “Decay of the Fourier transform of surfaces with vanishing curvature,” <i>Mathematische Zeitschrift</i>, vol. 257, no. 2. Springer, pp. 261–294, 2007.","short":"L. Erdös, M. Salmhofer, Mathematische Zeitschrift 257 (2007) 261–294.","chicago":"Erdös, László, and Manfred Salmhofer. “Decay of the Fourier Transform of Surfaces with Vanishing Curvature.” <i>Mathematische Zeitschrift</i>. Springer, 2007. <a href=\"https://doi.org/10.1007/s00209-007-0125-4\">https://doi.org/10.1007/s00209-007-0125-4</a>.","apa":"Erdös, L., &#38; Salmhofer, M. (2007). Decay of the Fourier transform of surfaces with vanishing curvature. <i>Mathematische Zeitschrift</i>. Springer. <a href=\"https://doi.org/10.1007/s00209-007-0125-4\">https://doi.org/10.1007/s00209-007-0125-4</a>","mla":"Erdös, László, and Manfred Salmhofer. “Decay of the Fourier Transform of Surfaces with Vanishing Curvature.” <i>Mathematische Zeitschrift</i>, vol. 257, no. 2, Springer, 2007, pp. 261–94, doi:<a href=\"https://doi.org/10.1007/s00209-007-0125-4\">10.1007/s00209-007-0125-4</a>."},"date_created":"2018-12-11T11:59:25Z","_id":"2752","status":"public","intvolume":"       257"}