Estimate for a Rearrangement of a Function Satisfying the “Reverse Jensen Inequality”

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.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 158–169, February, 2005.     

Estimates of Oscillations of the Hardy Transform

For the Hardy transform of a nonincreasing function we obtain a sharp two-sided estimate of the BLO-norm and sharp inequalities between the BMO- and the BLO-norms of a nonincreasing function. A well-known lower bound for the BMO-norm of the Hardy transform is improved on the basis of these inequalities.     

Self-improvement of summability factors of functions satisfying the reverse Hölder inequality in limit cases

We show that the best summability factors of functions that satisfy the reverse H?lder inequality in limit cases can be obtained from the nonlimit case by passing to the limit.     

Spin-reorientation transition in TbCo5

Nearly single-phase samples of compound TbCo_{5 + δ} (where δ = 0) are obtained and certified in the poly-and monocrystalline state. The latent heat is measured on these samples for the first time in the region of the spin-reorientation phase transition using differential scanning calorimetry. The latent heat of the transition is found to be 1.3 ± 0.2 kJ/kg. The experimental data are compared with the theoretical results obtained in the framework of the single-ion theory (Q _L = 1.1 kJ/kg). It is found that the discrepancy is insignificant to within the experimental error.     

On the Reverse Hölder inequality

We obtain exact positive and negative exponents of integrability of a function satisfying the reverse weighted Hölder inequality on parallelepipeds.     

Maximal function f# being in an Orlicz class

Translated from Matematicheskie Zametki, Vol. 46, No. 2, pp. 66–75, August, 1989.     

Estimates of Oscillations for the Conjugate Hardy Transform and for the Calderon Transform

For the conjugate Hardy transform and for the Calderon transform, the BLO-norms are calculated and two-sided estimates of the norms in the BMO are obtained, most of which are exact. Bibliography: 9 titles.     

Riesz rising sun lemma for several variables and the John-Nirenberg inequality

We obtain a multidimensional analog of the well-known Riesz rising sun lemma. We prove a more precise version of this lemma for space dimension d = 2 . We use these lemmas to establish an anisotropic analog of the John-Nirenberg inequality for functions of bounded mean oscillation with an exact constant in the exponent. Earlier, this exact constant was only known in the one-dimensional case.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 53–66.Original Russian Text Copyright © 2005 by A. A. Korenovskii.This revised version was published online in April 2005 with a corrected issue number.