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On solvability of the inhomogeneous Cauchy-Riemann equation in classes of functions bounded with weight and a system of weights. (Russian) Zbl 0851.35026
The author studies distributional solutions of the nonhomogeneous Cauchy-Riemann equation \[ {\partial f\over \partial \overline z}= g,\quad \text{where} \quad {\partial\over \partial \overline z}= {1\over 2} \Biggl({\partial\over \partial x}- i {\partial\over \partial y}\Biggr),\quad (z= x+ iy).\tag{1} \] In the first part of the paper, conditions for the existence of bounded solutions are derived. In the second part, this existence result is applied to generators of spaces of analytic functions.

MSC:
35F05 Linear first-order PDEs
30E25 Boundary value problems in the complex plane
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