Mean oscillations of the logarithmic function

The main property of functions with bounded mean oscillations-viz. the exponential decay of the distribution function, is considered. This property is represented by the John–Nirenberg inequality but the exact constant in the exponent is known only for the functions defined on those intervals which...

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Bibliographic Details
Published inRicerche di matematica Vol. 62; no. 1; pp. 81 - 90
Main Authors Didenko, Victor D., Korenovskyi, Anatolii A., Tuah, Nor Jaidi
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 01.06.2013
Subjects
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Mean oscillations
42B25
John–Nirenberg inequality
26D10
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Summary:The main property of functions with bounded mean oscillations-viz. the exponential decay of the distribution function, is considered. This property is represented by the John–Nirenberg inequality but the exact constant in the exponent is known only for the functions defined on those intervals which are at least one-sided bounded. In the present paper, an estimate of this constant for the functions having bounded mean oscillation on the whole real line is given. Moreover, an estimate of mean oscillations for the even extension of the functions defined on a semi-axis is established.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-012-0141-5