It is well-known that the Hölder-Rogers inequality implies the Minkowski inequality. Infantozzi [6] observed implicitely and Royden [15] proved explicitely that the reverse implication is also true. In this note we discuss and give a new proof of this perhaps surprising fact. Mathematics subject classification (2000): 26D15.

The main purpose of this paper is to establish with a constructive proof the following Hölder-type inequality: let A be a uniformly complete Φ-algebra, T be a positive linear functional, and p, q be rational numbers such that p−1 + q−1 = 1. Then the inequality T (|fg|) ≤ (T (|f |)) (T (|g|)) holds for all f, g ∈ A.

In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev sp...

We present dimension-free reverse Hölder inequalities for strong Ap weights, 1 ≤ p < ∞. We also provide a proof for the full range of local integrability of A1 weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no atoms. For p =∞, we also provide a reverse Hölder inequality for certain product ...

with equality if and only if the sequences ai and bi are proportional. The Aczél inequality (1) plays an important role in the theory of functional equations in non-Euclidean geometry. During the past years, many authors have given considerable attention to this inequality, its generalizations and applications [2-11]. As an example, the Hölder-like generalization of the Aczél inequality (1), de...

In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev sp...

We obtain central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities. The proofs are based on the Hölder-Young-Brascamp-Lieb inequality. AMS 2000 Classification: 60F05, 62M10, 60G15, 62M15, 60G10, 60G60