SOME RESULTS RELATED WITH POISSON-SZEGÄO KERNEL AND BEREZIN TRANSFORM

• 발행기관: 충청수학회
• 저자명: Gye Tak Yang Ki Seong Choi
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 24, No. 3, 417~426쪽, 전체 10쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2011.08.30

영문 초록

Let ¹ be a ¯nite positive Borel measure on the unit ball B ½ Cn and º be the Euclidean volume measure such that º(B) = 1. For the unit sphere S = fz : jzj = 1g, ¾ is the rotation-invariant measure on S such that ¾(S) = 1. Let P[f] be the Poisson-SzegÄo integral of f and ~¹ be the Berezin transform of ¹. R this paper, we show that if there is a constant M > 0 such that B jP[f](z)jpd¹(z) · M R B jP[f](z)jpdº(z) for all f 2 Lp(¾), then k ~¹ k1´ supz2B R j¹~(z)j < 1; and we show that if k ¹~ k1< 1; thenB jP[f](z)jpd¹(z) · C k ~¹ k1 RS jf(³)jpd¾(³) for some constantC.

목차

1. Introduction

2. Results related with Poisson-SzegÄo kernel

3. Berezin transform of ¹