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Korenovskii, Anatolii Aleksandrovich

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Total publications: 10
Scientific articles: 10

Number of views:
This page:1039
Abstract pages:2851
Full texts:1186
References:205
Associate professor
Candidate of physico-mathematical sciences (1988)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 13.02.1958
E-mail:
Keywords: classes of functions of Muckenhoupt, Gehring, Gurov–Reshetnyak, BMO; operators of Hilbert, Hardy, Calderon; maximal operators; weighted inequalities; covering lemmas; equimeasurable rearrangements of functions.

Subject:

The boundedness of the maximal Hilbert transform in BMO is proved. The behavior of the Fefferman–Stein maximal function in Orlicz spaces is investigated. The exact exponent in John–Nirenberg's inequality in one-dimensional case is found. The exact estimations of equimeasurable rearrangements of functions from Gehring and Muckenhoupt's classes are received in one-dimensional case, on the basis of which the limiting exponents of summability of functions from these classes are found. The lower and upper estimations of BMO-norm of Hardy transform and similar transforms are specified.

Biography

Graduated from Faculty of Mathematics and Mechanics of I. I. Mechnikov Odessa State University in 1979 (department of computing mathematics). Ph.D. thesis was defended in 1988.

   
Main publications:
  • A. A. Korenovskii. On the one-dimensional Muckenhoupt condition $A_\infty$. C. R. Acad. Sci. Paris. 1995, 320 (I), 19–24.

http://www.mathnet.ru/eng/person13264
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List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/262535

Publications in Math-Net.Ru
2007
1. A. A. Korenovskii, “On the Reverse Hölder Inequality”, Mat. Zametki, 81:3 (2007),  361–373  mathnet  mathscinet  zmath  elib; Math. Notes, 81:3 (2007), 318–328  isi  scopus
2005
2. A. A. Korenovskii, “Riesz rising sun lemma for several variables and the John–Nirenberg inequality”, Mat. Zametki, 77:1 (2005),  53–66  mathnet  mathscinet  zmath  elib; Math. Notes, 77:1 (2005), 48–60  isi  scopus
2003
3. A. A. Korenovskii, “Relation between the Gurov–Reshetnyak and the Muckenhoupt function classes”, Mat. Sb., 194:6 (2003),  127–134  mathnet  mathscinet  zmath; Sb. Math., 194:6 (2003), 919–926  isi  scopus
2002
4. A. A. Korenovskii, “Estimates of Oscillations of the Hardy Transform”, Mat. Zametki, 72:3 (2002),  383–395  mathnet  mathscinet  zmath; Math. Notes, 72:3 (2002), 350–361  isi  scopus
2001
5. A. A. Korenovskii, “Estimates of oscillations of the conjugate Hardy transform and Calderon transform”, Zap. Nauchn. Sem. POMI, 282 (2001),  106–117  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 120:5 (2004), 1704–1710
1992
6. A. A. Korenovskii, “The reverse Hölder inequality, the Muckenhoupt condition, and equimeasurable rearrangements of functions”, Dokl. Akad. Nauk, 323:2 (1992),  229–232  mathnet  mathscinet  zmath
7. A. A. Korenovskii, “The exact continuation of a reverse Hölder inequality and Muckenhoupt's conditions”, Mat. Zametki, 52:6 (1992),  32–44  mathnet  mathscinet  zmath; Math. Notes, 52:6 (1992), 1192–1201  isi
1990
8. A. A. Korenovskii, “On the connection between mean oscillation and exact integrability classes of functions”, Mat. Sb., 181:12 (1990),  1721–1727  mathnet  mathscinet  zmath; Math. USSR-Sb., 71:2 (1992), 561–567  isi
1989
9. A. A. Korenovskiĭ, “Mean oscillations and the Hilbert transform”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, 2,  28–41  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 33:2 (1989), 32–44
10. A. A. Korenovskii, “Maximal function $f^#$ being in an Orlicz class”, Mat. Zametki, 46:2 (1989),  66–75  mathnet  mathscinet  zmath; Math. Notes, 46:2 (1989), 620–626  isi

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