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PL(Ω,ω)条件与APL(Ω,ω)条件的等价关系

The Equivalence of PL(Ω,ω)and APL(Ω,ω)Conditions
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摘要 代数族V上关于特殊的函数u=log(1+|z|)的Phragmén-Lindelf条件PL(Ω)与APL(Ω)条件之间的关系已有很多研究,为更好地研究常系数线性偏微分算子右逆的性质提供了新的途径和方法.对更为一般的关于权函数ω(z)的Phragmén-Lindelf条件,借助代数族V的正则点上的多重次调和函数u,得到了PL(Ω,ω)条件与APL(Ω,ω)条件的等价性,通过选择适当的Phragmén-Lindelf条件更好地刻画了常系数线性偏微分算子P(D)的线性连续右逆的存在性. Some recent papers have investigated the relationship between PL（Ω） and APL（Ω） for special functions u of the form u = log（1 ＋｜z｜） in algebraic variety V, which have provided new approach and method for studying the properties of right inverse of constant coefficient linear partial differential operators. For more general Phragmon-Lindelof condition for weight function ω （z）, with the help of plurisubharmonic functions u at the regular points of V, the equivalence between PL（D） and APL（g2） conditions was ob- tained. Therefore, the existence of linear continuous right inverse for constant coefficient linear partial differ- ential operators P（D） can be characterized using suitable Phragmon-Lindelof condition.
作者 张婧 王光
机构地区 太原大学教育学院数学系 山西大学数学科学学院
出处 《中北大学学报（自然科学版）》 CAS 北大核心 2013年第5期548-550,554,共4页 Journal of North University of China(Natural Science Edition)
关键词 Phragmen-Lindelof条件 权函数 多重次调和函数 代数族 Phragmen-Lindelof condition weight function plurisubharmonic function algebraic variety
分类号 O175.2 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Braun R W, Meise R, Tayloy B A. Algebraic varieties on which the classical Phragm6n-Lindel6f estimaties hold for plurisubharmonic functions [ J ]. Math. Z, 1999, 232: 103-135.
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  • 3Meise R, Tayloy B A, Vogt D. Characterization of the linear partial operators with constant eoe[[icients that ad- mit a continuous linear right inverse[J]. Ann. Inst. Fou- rier(Grenoble), 1990, 40. 619-655.
  • 4Meise R, Tayloy B A. Phragmen-lindelof conditions for gragh varieties[J]. Result. Math., 1999, 36: 121-148.
  • 5Meise R, Tayloy B A, Vogt D. Phragmen-Lindelof prin- ciples on algebraic varieties[J ]. J. Amer. Math. Soc. , 1998, 11: 1-39.
  • 6Meise R, Tayloy B A, Vogt D. Equivalence of analytic and plurisubharmonic Phragmen-Lindelof conditions[J]. Proceedings of Symposia in Pure Mathematics, 1991, 52 : 287-308.
  • 7Hormander L. Complex Analysis in Several Variables [M]. 2nd. North Holland, 1973.
  • 8张婧,王光.Phragmén-Lindelf条件关于两个独立变量扰动的一个必要条件[J].中北大学学报（自然科学版）,2011,32(1):92-95. 被引量：2
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二级参考文献5

  • 1Braun R W,Meise R,Tayloy B A.Algebraic varieties on which the classical Phragmén-Lindelf estimaties hold for plurisubharmonic functions[J].Math.Z.,1999,232:103-135.
  • 2Meise R,Tayloy B A,Vogt D.Characterization of the linear partial operators with constant coefficients that admit a continuous linear right inverse[J].Ann.Inst.Fourier(Grenoble),1990,40:619-655.
  • 3Meise R,Tayloy B A,Vogt D.Phragmén-Lindelf principles on algebraic varieties[J].J.Amer.Math.Soc.,1998,11:1-39.
  • 4Braun R W,Meise R,Tayloy B A.A perturbation result for linear differential operators admitting a global right inverse on D'[J].Analysis,Geometry,Number Theory:The Math of Leon Ehrenpreis,Contemporary Math.,2000,251:93-106.
  • 5Braun R W,Meise R,Tayloy B A.Characterization of the homogeneous polynomials P for which (P+Q)(D) admits a comtinuous linear right inverse for all perturbations Q[J].Pacific.J.Math.,2000,192:201-218.

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中北大学学报（自然科学版）
2013年 第5期

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