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Oscillation and Nonoscillation Criteria for a Half-Linear Difference Equation of the Second Order and the Extended Discrete Hardy Inequality
We establish oscillatory properties of a half-linear difference equation of the second order with the help of a suitable extension of the weighted...
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An Improved One-Dimensional Hardy Inequality
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a...
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The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces
We introduce a discrete version of weighted Morrey spaces, and discuss the inclusion relations of these spaces. In addition, we obtain...
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A first order proof of the improved discrete Hardy inequality
We give an alternative first order proof of the improved discrete Hardy inequality recently found by Keller, Pinchover, and Pogorzelski.
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A reverse extended Hardy–Hilbert’s inequality with parameters
In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct...
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Cauchy Formulae and Hardy Spaces in Discrete Octonionic Analysis
In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order...
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On Iterated Discrete Hardy Type Inequalities for a Class of Matrix Operators
In this paper, we discuss new iterated discrete inequalities of Hardy type involving matrix kernels. Under some conditions on matrix entries of the...
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Weighted Discrete Hardy Inequalities on Trees and Applications
In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on Hölder- α domains, where the weights are powers of...
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Some remarks on dimension-free estimates for the discrete Hardy—Littlewood maximal functions
Dependencies of the optimal constants in strong and weak type bounds will be studied between maximal functions corresponding to the Hardy—Littlewood...
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On the sharp Hardy inequality in Sobolev–Slobodeckiĭ spaces
We study the sharp constant in the Hardy inequality for fractional Sobolev spaces defined on open subsets of the Euclidean space. We first list some...
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On the improvements of Hardy and Copson inequalities
In this current work, we revisit the recent improvements of the discrete Hardy’s inequality in one dimension and establish an extended improved...
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Weighted Discrete Hardy’s Inequalities
We give a short proof of a weighted version of the discrete Hardy inequality. This includes the known case of classical monomial weights with optimal...
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Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Its Applications to Hardy-Littlewood Inequalities
Let A be a general expansive matrix and X be a ball quasi-Banach function space on ℝ n , whose certain power (namely its convexification) supports a...
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A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the...
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A new reverse Hardy–Hilbert inequality with the power function as intermediate variables
In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct...