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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag New York
About this chapter
Cite this chapter
Agarwal, R.P., Ding, S., Nolder, C. (2009). Estimates for Jacobians. In: Inequalities for Differential Forms. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68417-8_8
Download citation
DOI: https://doi.org/10.1007/978-0-387-68417-8_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-56388-6
Online ISBN: 978-0-387-68417-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)