On solvability of the inhomogeneous Cauchy-Riemann equation in classes of functions bounded with weight and a system of weights. (Russian) Zbl 0851.35026

Epifanov, O. V.

Mat. Zametki 51, No. 1, 83-92 (1992).

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

Keywords:

inhomogeneous Cauchy-Riemann equation