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arXiv · 2009.02052

Bounded Extremal Problems in Bergman and Bergman-Vekua spaces

Briceyda Delgado·Juliette Leblond
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Abstract

We analyze Bergman spaces A p f (D) of generalized analytic functions of solutions to the Vekua equation $\partial$w = ($\partial$f /f)w in the unit disc of the complex plane, for Lipschitz-smooth non-vanishing real valued functions f and 1 < p < $\infty$. We consider a family of bounded extremal problems (best constrained approximation) in the Bergman space A p (D) and in its generalized version A p f (D), that consists in approximating a function in subsets of D by the restriction of a function belonging to A p (D) or A p f (D) subject to a norm constraint. Preliminary constructive results are provided for p = 2.

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Briceyda Delgado, Juliette Leblond. 2020-09-04. Bounded Extremal Problems in Bergman and Bergman-Vekua spaces. https://arxiv.org/abs/2009.02052

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