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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Published in | Ricerche di matematica Vol. 62; no. 1; pp. 81 - 90 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Milan
Springer Milan
01.06.2013
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0035-5038 1827-3491 |
DOI: | 10.1007/s11587-012-0141-5 |