The Hilbert-type integral inequalities with a homogeneous kernel of -degree.
The inequalities in variables.
The inequality of Milne and its converse. II.
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 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 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.
The scalar Oseen operator in
This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in theory.
The Schur-convexity of Stolarsky and Gini means.
The sharp Sobolev inequality in quantitative form
The Uncertainty Principle: A Mathematical Survey.
The weighted square integral inequalities for the first derivative of the function of a real variable.
Three mappings related to Chebyshev-type inequalities.
Three--parameter weighted Hardy type inequalities.
Time scale integral inequalities similar to Qi's inequality.
Time-scale integral inequalities.