Korenovskii A. A.
Ukr. Mat. Zh. - 2019. - 71, № 2. - pp. 246-260
The relative mean integral oscillations of a nondecreasing equimeasurable rearrangement are estimated from above via the same oscillations of the original function. On the basis of this estimate, we establish a lower order-exact estimate for the rate of decrease (vanishing) of the rearrangement.
Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1607-1619
We find the “norm” of a power function in the Gurov – Reshetnyak class on the real line. Moreover, as a result of numerical experiments, we establish a lower bound for the norm of the operator of even extension from the semiaxis onto the entire real line in the Gurov – Reshetnyak class.
Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 628-635
We establish exact bounds for the positive and negative exponents of summability of the power mean of a function in the case where this mean satisfies the reverse Jensen inequality.
Self-improvement of summability factors of functions satisfying the reverse Hölder inequality in limit cases
Ukr. Mat. Zh. - 2010. - 62, № 4. - pp. 483–493
We show that the best summability factors of functions that satisfy the reverse Hölder inequality in limit cases can be obtained from the nonlimit case by passing to the limit.
Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1418-1419
Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 158–169
We show that an equimeasurable rearrangement of any function satisfying the “reverse Jensen inequality” with respect to various multidimensional segments also satisfies the “reverse Jensen inequality” with the same constant.