The generalized Heron mean and its dual form.
The Hardy inequality with one negative parameter.
The Hardy-Landau-Littlewood inequalities with less smoothness.
The HELP inequality for Hamiltonian systems.
The Hermite-Hadamard type inequality of GA-convex functions and its application.
The Hilbert-type integral inequalities with a homogeneous kernel of -degree.
The Hlawka-Djoković inequality and points in unitary spaces.
The inequalities in variables.
The inequality of Milne and its converse. II.
The inner periodic structure of a function.
The level function in rearrangement invariant spaces.
An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.
The mapping in normed linear spaces with applications to inequalities in analysis.
The maximal solution of a restricted subadditive inequality in numerical analysis.
The maximal theorem for weighted grand Lebesgue spaces
We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality holds with some c independent of f iff w belongs to the well known Muckenhoupt class , and therefore iff for some c independent of f. Some results of similar type are discussed for the case of small Lebesgue spaces....
The Muckenhoupt class A₁(R)
It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.
The optimal convex combination bounds of arithmetic and harmonic means for the Seiffert's mean.
The power mean and the logarithmic mean.
The q-gamma function for q > 1.
The ratio between the tail of a series and its approximating integral.
The role of an integral inequality in the study of certain differential equations.