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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.
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.