Abstract
Let p be a prime and given a kernel K:Fp×Fp→C, define a discrete integral operator as follows: T(f)(x)=∑y∈Fpf(y)K(x,y), where f is any complex-valued function defined on Fp. We proved that if the kernel K satisfies certain natural size condition and cancellation conditions, the l2→l2-operator norm of T is bounded by p−γ for some positive number γ. This result can be viewed as a discrete analogue of Hörmander theorem. As an application, we recovered a power-saving estimate of certain bilinear average operator in finite fields by X. Li, Sawin and the author.
Original language | English (US) |
---|---|
Pages (from-to) | 22-31 |
Number of pages | 10 |
Journal | Finite Fields and Their Applications |
Volume | 59 |
DOIs | |
State | Published - Sep 2019 |
Externally published | Yes |
Keywords
- Bilinear operator
- Decay
- Finite fields
- Linear operator
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics