학술저널
COMPACT OPERATOR RELATED WITH POISSON-SZEGÄo INTEGRAL
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 20, No. 3
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2007.09333 - 342 (10 pages)
- 0
Suppose that ¹ is a ¯nite positive Borel measure on the unit ball B ½ Cn. The boundary of B is the unit sphere S = fz : jzj = 1g. Let ¾ be the rotation-invariant measure on S such that ¾(S) = 1. In this paper, we will show that if sup³2S R B P(z; ³)d¹(z) < 1 where P(z; ³) is the Poission-SzegÄo kernel for B, then ¹ is a Carleson measure. We will also show that if sup³2S R B P(z; ³)d¹(z) < 1, then the operator T such that T(f) = P[f] is compact as a mapping from Lp(¾) into Lp(B; d¹).
1. Introduction
2. Carleson measure and Poisson integral
3. Compact operator
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