# American Institute of Mathematical Sciences

January & February  2004, 10(1&2): 201-210. doi: 10.3934/dcds.2004.10.201

## Complex Neumann type boundary problem and decomposition of Lebesgue spaces

 1 Moscow Power Engineering Institute, Moscow, Russian Federation

Received  May 2003 Revised  September 2003 Published  October 2003

In this article, we study the generalization of the the decomposition $W_p^m(G)=\mathcal O_p^m(G)\oplus\partial W_{p,0}^{m+1}(G), p>1,m=0,\pm 1,\cdots$ to the case of several complex variables. More precisely, we consider the Lebesgue space $L_2(G)$ and prove that the above decomposition is closely related to the solvability of a complex Neumann problem whose solvability is equivalent to the complex version of Poincaré's inequality.
Citation: Julii A. Dubinskii. Complex Neumann type boundary problem and decomposition of Lebesgue spaces. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 201-210. doi: 10.3934/dcds.2004.10.201
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