A distinction between the paraboloid and the sphere in weighted restriction

• Alex Iosevich ^[1] ; Ruixiang Zhang ^[2]
  1. [1] University of Rochester

     University of Rochester

     City of Rochester, Estados Unidos

     
  2. [2] University of California System

     University of California System

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 3, 2026
• Idioma: inglés
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• Resumen

  • For several weights based on lattice point constructions in Rd (d > 2), we prove that the sharp L2 weighted restriction inequality for the sphere is very different than the corresponding result for the paraboloid. The proof uses Poisson summation, linear algebra, and lattice counting. We conjecture that the L2 weighted restriction is generally better for the circle for a wide variety of general sparse weights.