Global existence of analytic solutions to the Cauchy problem in a complex domain

We present results on the global existence of analytic solutions to the Cauchy problem in starshaped or convex complex domains. No growth conditions are imposed. Our results rely on a notion of solution-tube that we introduce. à la mémoire de Jean Leray     

M.Riesz定理的注记

设u(z)是单位圆内的实值调和函数 ,若 p_平均Mp(r ,u) =12π∫2π0｜u(reiθ) ｜pdθ1 p <∞ ,则称u(z) ∈hp( 1

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