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Multidimensional Hardy-type inequalities on time scales with variable exponents
(Journal article; Peer reviewed, 2019)
A new Jensen inequality for multivariate superquadratic functions is derived and proved. The derived Jensen inequality is then employed to obtain the general Hardy-type integral inequality for superquadratic and subquadratic functions of several variables.
Hardy-type inequalities over balls in R^N for some bilinear and iterated operators
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
Some new multidimensional Hardy-type inequalites are proved
and discussed. The cases with bilinear and iterated operators are considered
and some equivalence theorems are proved.
Some Fourier inequalities for orthogonal systems in Lorentz–Zygmund spaces
(Journal article; Peer reviewed, 2019-06-13)
A number of classical inequalities and convergence results related to Fourier coefficients with respect to unbounded orthogonal systems are generalized and complemented. All results are given in the case of Lorentz–Zygmund spaces.
Equivalent integral conditions related to bilinear Hardy-type inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
Infinitely many, even scales of, equivalent conditions are derived to characterize the bilinear Hardy-type inequality under various ranges of parameters.