# Affine Moserâ€“Trudinger and Morreyâ€“Sobolev inequalities

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We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder's, Cauchy-Schwarz's, and Minkowski's...