SHARP Lp → Lr ESTIMATES OF RESTRICTED AVERAGING OPERATORS OVER CURVES ON PLANES IN FINITE FIELDS

• 발행기관: 충청수학회
• 저자명: Doowon Koh
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 28, No. 2, 251~259쪽, 전체 9쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2015.05.30

국문 초록

Let Fdq be a d-dimensional vector space over a finite field Fq with q elements. We endow the space Fdq with a normalized counting measure dx. Let σ be a normalized surface measure on an algebraic variety V contained in the space (Fdq, dx). We define the restricted averaging operator A V by A V f (x) = f * σ(x) for x ∈ V, where f : (Fdq, dx) → C. In this paper, we initially investigate L p → L r estimates of the restricted averaging operator A V . As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on F play a crucial role in proving our results.

목차

1. Introduction

2. Statement of the main result

3. Review of extension problems for curves

4. Proof of the main theorem (Theorem 2.3)

키워드

lgebraic curves finite fields restricted averaging operators.