Bergman spaces for the bicomplex Vekua equation with bounded coefficients

IF 1.2 3区 数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2024-11-04 DOI:10.1016/j.jmaa.2024.129025
Víctor A. Vicente-Benítez
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Abstract

We develop the theory for the Bergman spaces of generalized Lp-solutions of the bicomplex-Vekua equation W=aW+bW on bounded domains, where the coefficients a and b are bounded bicomplex-valued functions. We study the completeness of the Bergman space, the regularity of the solutions, and the boundedness of the evaluation functional. For the case p=2, the existence of a reproducing kernel is established, along with a representation of the orthogonal projection onto the Bergman space in terms of the obtained reproducing kernel, and an explicit expression for the orthogonal complement. Additionally, we analyze the main Vekua equation (a=0, b=ff with f being a non-vanishing complex-valued function). Results concerning its relationship with a pair of conductivity equations, the construction of metaharmonic conjugates, and the Runge property are presented.
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具有有界系数的二重维库阿方程的伯格曼空间
我们发展了有界域上二复-Vekua 方程 ∂‾W=aW+bW‾ 的广义 Lp 解的伯格曼空间理论,其中系数 a 和 b 是有界的二复值函数。我们研究了伯格曼空间的完备性、解的正则性和求值函数的有界性。在 p=2 的情况下,我们确定了重现核的存在,并用得到的重现核表示了伯格曼空间的正交投影,以及正交补码的明确表达式。此外,我们还分析了主 Vekua 方程(a=0, b=∂‾ff,f 为非消失的复值函数)。结果涉及它与一对传导方程的关系、元谐共轭的构造以及 Runge 特性。
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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Editorial Board Editorial Board Editorial Board Editorial Board Bivariate homogeneous functions of two parameters: Monotonicity, convexity, comparisons, and functional inequalities
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