NOTE ON THE OPERATOR b P ON Lp(@D)

• 발행기관: 충청수학회
• 저자명: Ki Seong Choi
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 21, No. 2, 269~278쪽, 전체 10쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2008.06.30

영문 초록

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).

목차

1. Introduction

2. Bounded operator b P on Lp(@D), 1  p < 1

3. Unbounded operator b P on L1(D)

References