A bound for certain bibasic sums and applications.
A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.
We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.
A Carlson type inequality with blocks and interpolation
An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of “blocks” and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre’s interpolation functor (see [26]) and its Gagliardo closure on couples of...
A certain modification of Hardy's inequality
A characterization of a two-weight inequality for discrete two-dimensional Hardy operators.
A characterization of the orthogonal polynomials.
A class of -conservative matrices.
A class of inequalities related to the angle bisectors and the sides of a triangle.
A class of logarithmically completely monotonic functions related to and an application.
A Class of Means and Related Inequalities.
A Cohen-type inequality for Jacobi-Sobolev expansions.
A companion of Ostrowski's inequality for mappings whose first derivatives are bounded and applications in numerical integration
A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials
We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...
A computer proof of Turán's inequality.
A condition implying boundedness and VMO for a function f
Some boundedness and VMO results are proved for a function f integrable on a cube , starting from an integral bound.
A conjecture of Schoenberg.
A continuous and a discrete variant of Wirtinger's inequality.
A converse inequality of Hölder type.
A converse of Minkowski's type inequalities.
A converse to some inequalities and approximations in the theory of Stieltjes and stochastic integrals, and for nth derivatives