Geodesic
On solvability of inhomogeneous Cauchy--Riemann equation in functional spaces with a~system of uniform estimates
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2015), pp. 77-82

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We obtain an analog of the Hörmander theorem on solvability of the $\overline\partial$-problem in spaces of functions satisfying a system of uniform estimates. The result is formulated in terms of the weight sequence which determines the space. We give some applications for multipliers of projective and inductive-projective weight spaces of entire functions and for convolution operators in the Roumieu spaces of ultradifferentiable functions.
Keywords: inhomogeneous Cauchy–Riemann equation, projective weight spaces, convolution operators, ultradifferentiable functions.
Mots-clés : multipliers 
@article{IVM_2015_10_a8,
     author = {D. A. Polyakova},
     title = {On solvability of inhomogeneous {Cauchy--Riemann} equation in functional spaces with a~system of uniform estimates},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {77--82},
     publisher = {mathdoc},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_10_a8/}
}
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D. A. Polyakova. On solvability of inhomogeneous Cauchy--Riemann equation in functional spaces with a~system of uniform estimates. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2015), pp. 77-82. http://geodesic.mathdoc.fr/item/IVM_2015_10_a8/