EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM
EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM

영남수학회
East Asian mathematical journal
Vol.19 No.1
2003.01

73 - 80 (8 pages)

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Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM
EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM

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EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM

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EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM
EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM

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