Conjugate functions, L^p-norm like functionals, the generalized Hölder inequality, Minkowski inequality and subhomogeneity

The Brunn-Minkowski-Type Inequality

The Brunn-Minkowski Inequality

In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of Rn, and deserves to be better known. This guide explains the relationship between the Brunn-Minkowski inequality and other inequalities in geometry and analysis, an...

the brunn-minkowski-type inequality

Hölder continuity of a parametric variational inequality

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

Another View on the Hölder Inequality

Every diagonal matrix D yields an endomorphism on the n-dimensional complex vector space. If one provides the n with Hölder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of normed spaces. We generalize the Hölder norms for negative values, this leads to a proof of an extended version of the Hölder inequality. Finally, we formulate this v...