Denseness of domains of differential operators in Sobolev spaces.
Derivatives of Catalan related sums.
Determination of the best constant in an inequality of Hardy, Littlewood, and Pólya.
Diamond- Jensen's inequality on time scales.
Difference of general integral means.
Differences of weighted mixed symmetric means and related results.
Differentiability from the representation formula and the Sobolev-Poincaré inequality
In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.
Differential estimate for -ary forms on closed orthants.
Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities
We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.
Discrete analogues of Wirtinger's inequality for a two-dimensional array
Discrete Inequalities of Generalized Wirtinger Type.
Discrete inequalities of Wirtinger's type for higher differences.
Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions.
Discretization and anti-discretization of rearrangement-invariant norms.
Distribution and rearrangement estimates of the maximal function and interpolation
There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous...
Disuguaglianze di Sobolev nello spazio iperbolico bidimensionale
Dokaz jedne nejednakosti J. Barkes-a
Domination in the families of Frank and Hamacher t-norms
Domination is a relation between general operations defined on a poset. The old open problem is whether domination is transitive on the set of all t-norms. In this paper we contribute partially by inspection of domination in the family of Frank and Hamacher t-norms. We show that between two different t-norms from the same family, the domination occurs iff at least one of the t-norms involved is a maximal or minimal member of the family. The immediate consequence of this observation is the transitivity...
Double exponential integrability, Bessel potentials and embedding theorems
This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
Dragomir-Agarwal type inequalities for several families of quadratures.