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Estimates for Jacobians

  • Ravi P. AgarwalEmail author
  • Shusen Ding
  • Craig Nolder
Chapter

Abstract

In this chapter, we first present some integral inequalities related to a strictly increasing convex function on [0, ∞) and then improve the Hölder inequality with L p (log L) α (Ω)-norms to the case 0 < p, q < ∞. Next, we prove L p (log L) α (Ω)-integrability of Jacobians. We also show that the integrability exponents described in Theorem 8.2.7 are the best possible.

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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of MathematicsSeattle UniversitySeattleUSA
  3. 3.Department of MathematicsFlorida State UniversityTallahasseeUSA

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