Azerbaijan National Academy of Science
The first website of Azerbaijan (1995)
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Department of Mathematical analysis
| Phone | (+994 12) 5397579 | |
| Fax | (+994 12) 5390102 | |
| vagif.guliyev@imm.az, | ||
| Chief | Corr. member of ANAS, professor Vagif Sabir oglu Guliyev | |
| Total number of employees | 16 | |
| Basic activity directions | Studying operators connected with shift operator generated by maximal and fractional-maximal operators, integral operators of the Riesz potential type, integral operators of Hardy type, of the multi-dimensional mean-geometric operator, and Bessel, Dunkle, Laguerre, Gegenbauer operators and other diferential operators in various functional spaces;
Studying maxsimal operator, the potential type integral operators and singular integral operators in the generalized Orlicz-Morrey and Lebesgue and Morrey type spaces with variable exponent; Research integral operators of real analysis in the local type Morrey spaces. |
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| Main scientific achievements | Тhе boundedness of integral operators of real analysis, and also maximal and fractional-maximal operators, integral operators of the Riesz potential type, integral operators of Hardy type, of the multi-dimensial mean-geometric operator, and also Bessel, Dunkle, Lagerre, Gegenbauer operators and other diferential operators in various functional spaces were studied. Some properties of the Lebesgue and Morrey type spaces with a variable exponent are studied. The boundedness of the maxsimal operator, the potential type integral operators and singular integral operators in the Lebesgue and Morrey spaces with variable exponent was studied. Necessary and sufficient conditions on the parameter for the boundedness of integral operators of real analysis in the local Morrey type spaces were found. The obtained results were used for a priori estimations and regularization of the solutions of elliptic and parabolic equations in generalized Morrey spaces. A problem for finding the solutions of certain type differential equations in the Lebesgue spaces with a variable exponent and in weighted Lebesgue spaces were studied.
New Morrey-Lorentz local spaces were introduced and some embedding theorems in these spaces were obtained. It was shown that these spaces are not connected with the classical Morrey space and at certain intermediate values of parameters coincide with Marcinkewich spaces. Boundedness of maximal, fractional-maximal operators, potential operator and singular integral operators in local Morrey-Loretsz spaces was studied. Application of the results obtained for boundedness of integral operators in generalized Morrey spaces to regularity of the solutions of elliptic and parabolic type differential equations, was given. The criteria of statistical approximation of analytic functions in bounded domains were found by means of sequential linear positive operators. Order of approximation rate of functions by Bernstein-Khlodovskii polynomials and by Sasz operators were obtained. |
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