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Mutual estimates of L p -norms and the Bellman function.
- Source :
- Journal of Mathematical Sciences; Feb2009, Vol. 156 Issue 5, p766-798, 33p
- Publication Year :
- 2009
-
Abstract
- In this paper, we describe the range of the L<superscript>p</superscript>-norm of a function under fixed L<superscript>p</superscript>-norms with two other different exponents p and under a natural multiplicative restriction of the type of the Muckenhoupt condition. Particular cases of such results are simple inequalities as the interpolation inequality between two L<superscript>p</superscript>-norms as well as such nontrivial inequalities as the Gehring inequality or the reverse Hölder inequality for Mackenhoupt weights. The basic method of our paper is the search for the exact Bellman function of the corresponding extremal problem. Bibliography: 5 [ABSTRACT FROM AUTHOR]
- Subjects :
- NUMERICAL analysis
ARITHMETIC
EQUATIONS
INTERVAL analysis
MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 156
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 36197060
- Full Text :
- https://doi.org/10.1007/s10958-009-9288-3