Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals

نویسندگان

چکیده

We prove sharp estimates for Fourier transforms of indicator functions bounded open sets in $${\mathbb {R}}^n$$ with real analytic boundary, as well nontrivial lattice point discrepancy results. Both are derived from on hypersurface measures. Relations maximal averages discussed, connecting two conjectures Iosevich and Sawyer (Adv Math 132(1):46–119, 1997). also a theorem concerning the stability under function perturbations growth rate near zero. This result is an appropriate sense. It implies corresponding local integrablity negative powers

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ژورنال

عنوان ژورنال: Mathematische Annalen

سال: 2021

ISSN: ['1432-1807', '0025-5831']

DOI: https://doi.org/10.1007/s00208-021-02156-z