Journal of Mathematical Sciences

, Volume 156, Issue 5, pp 766–798 | Cite as

Mutual estimates of Lp-norms and the Bellman function


In this paper, we describe the range of the Lp-norm of a function under fixed Lp-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 Lp-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


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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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