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Complex Neumann type boundary problem and decomposition of Lebesgue spaces

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  • 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.
    Mathematics Subject Classification: 30E25.

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