Estimates for Jacobians
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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