Korenovs'kyj A. Mean oscillations, reverse inequalities, and equimeasurable rearrangements of functions

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0507U000146

Thesis Registration Form

0507U000146.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

01-03-2007

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

There are obtained the sharp estimate of the rearrangement of a function of bounded mean oscillation and the John - Nirenberg inequality with the sharp constant. The sharp estimates of the rearrangement of a function satisfying the Gurov - Reshetnyak condition and the reverse Jensen inequalities are obtained. There are found the sharp exponents of Gehring's and Muckenhoupt's classes, in which the Gurov - Reshetnyak class is enclosed, and the sharp bounds of the self-improvement of the exponents of classes of functions satisfying the reverse Holder inequality.

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Files

AVTOREFERAT--Aref.doc

AVTOREFERAT--TITUL.DOC

Tekst_dissertacii.pdf

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