학술저널
SOME RESULTS RELATED WITH POISSON-SZEGÄO KERNEL AND BEREZIN TRANSFORM
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 24, No. 3
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2011.08417 - 426 (10 pages)
- 2
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.
1. Introduction
2. Results related with Poisson-SzegÄo kernel
3. Berezin transform of ¹
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