Convexity of the zero-balanced Gaussian hypergeometric functions with respect to Hölder means.
Convexity of weighted Stolarsky means.
Convexity with given infinite weight sequences.
Convexity-like inequalities for averages in a convex set.
Convexity-like inequalities for averages in a convex set. (Summary).
Convex-like inequality, homogeneity, subadditivity, and a characterization of -norm
Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the -norm.
Corrections to the paper “The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces“
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted...
Critères de convexité et inégalités intégrales
Pour trois fonctions non-négatives intégrables sur , et , telles que , Borelll a établi l’inégalité . Nous déterminons les conditions précises où l’inégalité sera stricte. La clef de cette analyse est une nouvelle caractérisation des fonctions convexes mesurables.
Criteria of general weak type inequalities for integral transforms with positive kernels.
Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces.
Criteria on boundedness of matrix operators in weighted spaces of sequences and their applications.