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A note on Maz'ya-Verbitsky capacitary inequalities
We present a proof of Maz'ya-Verbitsky capacitary inequalities in terms of Bessel potentials. It will be seen that the proof mainly relies on the...
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Gagliardo–Nirenberg Inequalities in Lorentz Type Spaces
In this paper, we derive some new Gagliardo–Nirenberg type inequalities in Lorentz type spaces without restrictions on the second index of Lorentz...
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Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form
Our aim is to give Sobolev-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric...
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ON HARDY-TYPE INEQUALITIES AS AN INTELLECTUAL ADVENTURE FOR 100 YEARS
We describe some chosen ideas and results for more than 100 years prehistory and history of the remarkable development concerning Hardy-type...
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Hardy-Sobolev Inequalities with Dunkl Weights
We establish several identities and inequalities of Hardy type and Sobolev type with Dunkl weights. We also investigate the sharp constants and...
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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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Inequalities for Convex Functions and Isotonic Sublinear Functionals
In this paper, versions of the famous Jensen inequality for sublinear isotonic functionals are proved. The obtained results generalize classic...
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Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces
We will prove that for 1 < p < ∞ and 0 < λ < n , the central Morrey norm of the truncated centered Hardy-Littlewood maximal operator M γ c equals that...
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Characterization of Fractional Sobolev–Poincaré and (Localized) Hardy Inequalities
In this paper, we prove capacitary versions of the fractional Sobolev–Poincaré inequalities. We characterize localized variant of the boundary...
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Weighted Variation Inequalities for Singular Integrals and Commutators in Rearrangement Invariant Banach and Quasi-Banach Spaces
In order to study the boundedness of some operators in general function spaces which include Lorentz spaces and Orlicz spaces as special examples,...
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Weighted weak-type inequalities for maximal operators and singular integrals
We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional...
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Results for Retarded Nonlinear Integral Inequalities with Mixed Powers and Their Applications to Delay Integrodifferential Equations
We present new retarded nonlinear integral inequalities with mixed powers. The obtained inequalities can be used to study the property of boundedness...
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Boundedness of maximal function for weighted Choquet integrals
We study the boundedness of Hardy–Littlewood maximal function on the spaces defined in terms of Choquet integrals associated with weighted Bessel and...
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New Universal Inequalities for Eigenvalues of a Clamped Plate Problem
In this paper, we study the universal inequalities for eigenvalues of a clamped plate problem, and establish some new universal inequalities that are...
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A unified approach to inequalities for K-functionals and moduli of smoothness
The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach...
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Hardy–Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces
We establish a Hardy–Sobolev inequality for Riesz potentials of functions in Orlicz spaces.
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Novel results of Milne-type inequalities involving tempered fractional integrals
In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of...