학술저널
RESTRICTED AVERAGING OPERATORS IN THE FINITE FIELD SETTING
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 30, No. 2
-
2017.05259 - 272 (14 pages)
- 2
In this paper we study the mapping properties of the finite field restricted averaging operators to various algebraic vari-eties. We derive necessary conditions for the boundedness of the generalized restricted averaging operator related to arbitrary alge-braic varieties. It is shown that the necessary conditions are in fact sufficient in the specific case when the Fourier transform on varieties has enough decay estimates. Our work extends the known optimal result on regular varieties such as paraboloids and spheres to certain lower dimensional varieties.
1. Introduction
2. Statement of main results
3. Necessary conditions for A S,V (p → r) ≤ 1
4. Proofs of the main theorems (Theorem 2.2 and Theo-rem 2.5)
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