01.01.01 (Real analysis, complex analysis, and functional analysis)
classes of functions of Muckenhoupt, Gehring, Gurov–Reshetnyak, BMO; operators of Hilbert, Hardy, Calderon; maximal operators; weighted inequalities; covering lemmas; equimeasurable rearrangements of functions.
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.
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.
A. A. Korenovskii. On the one-dimensional Muckenhoupt condition $A_\infty$. C. R. Acad. Sci. Paris. 1995, 320 (I), 19–24.