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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