Volume inequalities for complex isotropic measures

Abstract

A new notion of complex isotropic measures is introduced and volume inequalities for their L p -cosine and their sine transform are established.

Dual mixed complex brightness integrals

“…Along the same line, for i > 2n − 1 and i 2n, the reversed inequality of (29) can be deduced directly via of follows from (12) and the reversed case of (30).…”

VOLUME INEQUALITIES FOR THE Lp-SINE TRANSFORM OF ISOTROPIC MEASURES

“…, b n denote orthonormal basis vectors of R n . Isotropic measures have been the focus of recent studies, in particular, in relation with a variety of extremal problems for convex bodies (see, e.g., [8,9,16,20,29,43,45] and the references therein).…”