Korenovsky Anatoly Alexandrovich (February 13, 1958 , p. Shevchenkovo, Kiliya district, Odessa region ) - a mathematician . Doctor of Physical and Mathematical Sciences ( 2007 ); Professor ( 2008 ); Head of the scientific school "Theory of Functions of Real and Complex Variables". Diploma of management of science and scientific activity of the Odessa regional state administration, Soros assistant professor.
| Korenovsky Anatoly Alexandrovich | |
|---|---|
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| Date of Birth | February 13, 1958 (61 years) |
| Place of Birth | with. Shevchenkovo , Kiliya district of Odessa region. ,  Ukrainian SSR |
| Scientific field | maths |
| Place of work | Odessa National I. Mechnikov University |
| Alma mater | Odessa State University. I.I. Mechnikova |
| Academic degree | doctor of physical and mathematical sciences |
| Academic title | Professor |
Content
Biography
Born February 13, 1958 in a. Shevchenko Kiliyskogo district of Odessa region . In 1979 , he graduated from the I. Mechnikov Odessa State University (now the I. Mechnikov Odessa National University ). 1979 - 1981 - Works as a software engineer at the Nikolaev Computing Center. Since 1983 he has been working at ONU. I.I. Mechnikov . Since 2009 - Head. Department of Mathematical Analysis .
In 1988 he defended his thesis "Properties of functions defined in terms of mean oscillations".
In 2007 he defended his doctoral thesis "Average oscillations, reversed irregularities and exactly measurable permutations" at the Institute of Mathematics of the National Academy of Sciences .
Anatoly Alexandrovich delivers lectures in such disciplines as: " Mathematical analysis ", "Theory of measure and integral", "Differential properties of functions of a real variable", "Weighted estimates for the maximal Hardy-Littlewood operator", "Functions with bounded mean oscillation", " properties of functions expressed in terms of mean oscillations "
Scientific Activities
The main direction in A. A. Korenovsky’s scientific activities is the theory of functions of a real variable, harmonic analysis.
A. Korenovsky's doctoral thesis is devoted to the study of extremal properties of classes of functions, which are denoted by conditional local characteristics. The main results of the work are as follows:
- a new proof of the F. Riss lemma about the rising sun is given. This proof is transferred to the case of multidimensional segments for any absolutely continuous measure;
- in the anisotropic case, an exact estimate is obtained for an equilibrium rearrangement of a function with a bounded mean oscillation. Based on this estimate, an exact constant was found in the exponent in the anisotropic John-Nirenberg inequality;
- the obtained estimates of oscillations of Hardy type transformations and Calderon transformations do not improve in some cases;
- the possibility of increasing the summability index of a function that satisfies the isotropic conditions of Gurov-Reshetnyak for any value of the class parameter and for any absolutely continuous measure is shown. The properties of the function that satisfies the analogue of the Gurov-Reshetnyak condition in terms of maximal functions are studied;
- for a function that satisfies the Gurov-Reshetnyak's anisotropic condition, an exact estimate is obtained for an equilibrium permutation. On the basis of this estimate, exact limit values of the Muckenhoupt and Goering classes are found, in which the Gurov-Reshetnyak class is embedded;
- in the one-dimensional case, the exact limits of self-improvement of the indicators of the classes of Goering and Muckenhoupt were found;
- found the exact limits of self-improvement of indicators for classes of functions that satisfy the inverse anisotropic Hölder inequality in the case of an arbitrary absolutely continuous measure.
Proceedings
- On the belonging of a maximal function to the Orlicz class / A. A. Korenovsky // Mat. notes. - 1989. - Vol. 46, No. 2. - P. 66-75.
- Average oscillations and the Hilbert transform / A. A. Korenovskiy // Izvestiya VUZ. Maths. - 1989. - № 2. - p. 28-40.
- On the relationship between mean oscillations and exact indicators of summability of functions / A. A. Korenovsky // Matem. compilation. - 1990. - V. 181, № 12. - P. 1721-1727.
- On the exact continuation of the inverse Hölder inequality and the Muckenhoupt condition / A. A. Korenovsky // Mat. notes. - 1992. - V. 52, № 6. - P. 32-44.
- Hölder's Inverse Inequality, the Muckenhoupt Condition and Equivariating Function Permutations / A. A. Korenovsky // Dokl. Academy of Sciences of the USSR. - 1992. - T. 323, No. 2. - P. 229-232.
- The multidimensional version of the Riesz lemma and some of its applications / A. A. Korenovsky // Volinsky Mathematical Bulletin. - 1996. - Vip. 3. - p. 50-55.
- On a generalization of the Gurov-Reshetnyak inequality / A. A. Korenovskiy // Theory of the num- ber of functions and consensus. - Kiev, 2000. - (Pr. In-that of mathematics of the National Academy of Sciences of Ukraine; vol. 31).
- Estimates of oscillations of the conjugate Hardy transform and Calderon transform / A. A. Korenovsky // Studies on linear operators and function theory. - SPb., 2001. - (Western scientific seminars POMI; vol. 282).
- On the estimation of the norm in the WMO Hardy – Littlewood transformations / A. A. Korenovsky // Theory of nominal functions and total nutrition. - K., 2002. - (Pr. Іn-that of mathematics of the National Academy of Sciences of Ukraine. Mathematics and consensus; v. 35).
- Estimates of oscillations of the Hardy transform / A. A. Korenovsky // Mat. notes. - 2002. - Vol. 72, No. 3.
- A note on the Gurov-Reshetnyak condition / A. A. Korenovskiy, AK Lerner, AM Stokolos // Math. Research Letters. - 2002. - Vol. 9, No. 5-6.
- On the spectral radius of convolution dilation operators / A. A. Korenovskiy, VD Didenko, SL Lee // J. Anal. Appl. - 2002. - Vol. 21, № 4.
- On the relationship between the classes of Gurov-Reshetnyak and Muckenhaupt functions / A. A. Korenovsky // Mat. Sat - 2003. - T. 194, No. 6. - P. 127-134.
- On the nesting of the Goering class in the Gurov-Reshetnyak class / A. A. Korenovsky // Vіsn. Odes. hold un-tu. Seriya: Fіz.-mat. sciences. - 2003. - V. 8, vip. 2
- On the class of Gurov-Reshetnyak's functions / A. A. Korenovsky // Problems and Functions and Functions. - Kiev, 2004. - (Zb. Pr. In-that of mathematics of the National Academy of Sciences of Ukraine; t. 1, No. 1).
- Estimates of Oscillations for the Conjugate Hardy Transform and for the Calderon Transform / A. A. Korenovskii // J. of Math. Science. - 2004. - Vol. 120, № 5.
- Riesz’s lemma “On the Rising Sun” for many variables and the John – Nirenberg inequality / A. A. Korenovsky // Mat. notes. - 2005. - T. 77, № 1. - p. 53-66.
- Estimation of the rearrangement of functions satisfying the “reverse Jensen inequality” / A. A. Korenovsky // Ukr. mat. Journal .. - 2005. - V. 57. No. 2. - P. 158-169.
- On the reverse Hölder inequality / A. A. Korenovsky // Mat. Notes. - 2007. - V. 81, № 3. - P. 361 - 373.
- Mean Oscillations and Equimeasurable Rearrangements of Functions / A. Korenovskii. - Heidelberg (Berlin): Springer-Verlag, 2007. - 188 p. - (Lecture Notes of the Union Matematica Italiana; Bd. 4).
- A course of lectures on mathematical analysis: at 2 pm / A. A. Korenovsky, V. I. Kolyada; Odes. nat un-t them. I.I. Mechnikova, Institute of Mathematics, Economics and Mechanics. - Odessa: Astroprint, 2010. - Part 1. - 367 p. ; Part 2 - 291 s.