A variant of a general inequality of the Hardy-Knopp type.
A Volterra inequality with the power type nonlinear kernel.
A weighted estimate for an intermediate operator on the cone of nonnegative functions.
A weighted inequality for derivatives on the half-line.
Adams inequality on metric measure spaces.
Almost everywhere convergence of the spherical partial Fourier integrals for radial functions.
Alternative characterisations of Lorentz-Karamata spaces
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
An embedding theorem for Sobolev type functions with gradients in a Lorentz space
The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
An extension of Stolarsky means to the multivariable case.
An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products.
An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products.
An inequality which arises in the absence of the mountain pass geometry.
An integral inequality for 3-convex functions.
An Integral Inequality Similar to Bellman-Bihari inequality
An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
An interpolation inequality involving Hölder norms.
An isoperimetric bound for a Sobolev constant
An two-well Liouville theorem.
An optimal 3-point quadrature formula of closed type and error bounds.
Analyse sur les boules d' un opérateur sous-elliptique.