Leonchik E. Oscillations of functions and differential-difference properties of singular integrals

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0404U001804

Thesis Registration Form

0404U001804.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

16-04-2004

Specialized Academic Board

К 41.051.05

Essay

The exact estimations for the mean oscillations of the essentially and weakly bounded functions are obtained. For that the necessary and sufficient conditions for Korneychuk inequality were found. The exact order estimations of singular integrals are found in terms of Calderon maximal function in case of the odd and summable kernels. The estimations equimeasurable rearrangement is obtained in terms of maximal function which tightly bound up with Muckenhoupt condition. The behaviour of Hardy-Littlewood and Fefferman-Stein maximal functions are investigated in a point of discontinuity as well

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