학술저널
NOTE ON THE OPERATOR b P ON Lp(@D)
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 21, No. 2
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2008.06269 - 278 (10 pages)
- 0
Let @D be the boundary of the open unit disk D in the complex plane and Lp(@D) the class of all complex, Lebesgue measurable function f for which { 1 2R −|f()|pd}1/p < 1. Let P be the orthogonal projection from Lp(@D) onto \n<0 ker an. For f 2 L1(@D), ˆ f(z) = 12 R − Pr(t − )f()d is the harmonic extension of f. Let b P be the composition of P with the harmonic extension. In this paper, we will show that if 1 < p < 1, then b P : Lp(@D) ! Hp(D) is bounded. In particular, we will show that b P is unbounded on L1(@D).
1. Introduction
2. Bounded operator b P on Lp(@D), 1 p < 1
3. Unbounded operator b P on L1(D)
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