Hardy Type Research Articles

Multiplicity Results of Solutions to the Fractional p-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type

This paper is devoted to establishing multiplicity results of nontrivial weak solutions to the fractional p-Laplacian equations of the Kirchhoff–Schrödinger type with Hardy potentials. The main features of the paper are the appearance of the Hardy potential and nonlocal Kirchhoff coefficients, and the absence of the compactness condition of the Palais–Smale type. To demonstrate the multiplicity results, we exploit the fountain theorem and the dual fountain theorem as the main tools, respectively.

HARDY INEQUALITIES AND IDENTITIES RELATED TO THE BAOUENDI-GRUSHIN VECTOR FIELDS AND LANDAU-HAMILTONIAN

In this paper, we present a weighted Hardy identity related to the Baouendi-Grushin vector fields and its applications in the context of differential inequalities. By selecting appropriate parameters, the Hardy identity related to the Baouendi-Grushin operator implies numerous sharp remainder formulae for Hardy type inequalities. In the commutative case, we obtain improved weighted Hardy inequalities in the setting of the Euclidean space. For example, in a special case, by dropping non-negative remainder terms, related to the Baouendi-Grushin operator, and choosing suitable parameters our identity allows us to derive an improved critical Hardy inequality for the radial derivative operator with a sharp constant that does not depend on the topological dimension. We employ the method of factorizing differential expressions, as used by Gesztesy and Littlejohn in [1]. In this paper, we demonstrate the application of the factorization method in the noncommutative Baouendi-Grushin setting. As an application of the Hardy identity related to the Baouendi-Grushin vector fields, we establish a Hardy inequality for the generalized Landau Hamiltonian (or the twisted Laplacian) with remainder terms.

On some characterizations of classical operators of composition Hardy type

In this paper, we study classical operators of composite Hardy type on Lp− space. Our focus is to discuss some operator theoretic properties of the classical operators of composite Hardy type. An attempt has been made to compute the nth approximation number of classical operators of composite Hardy type. Keywords: Classical operators of Composite Hardy type; Composition operator; Expectation operator; Radon- Nikodym derivative.

Complex Structure That Admits Complete Nevanlinna–Pick Spaces of Hardy Type

Abstract In this paper, we will characterize those sets, over which every irreducible complete Nevanlinna–Pick space enjoys that its multiplier and supremum norms coincide. Moreover, we will prove that, if there exists an irreducible complete Nevanlinna–Pick space of holomorphic functions on a reduced complex space $X$ whose multiplier algebra is isometrically equal to the algebra of bounded holomorphic functions (we will say that such a space is of Hardy type in this paper), then $X$ must be biholomorphic to the unit disk minus a zero analytic capacity set. This means that the Hardy space is characterized as a unique irreducible complete Nevanlinna–Pick space of Hardy type.

Quantitative Hardy inequalities for magnetic Hamiltonians

In this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these inequalities both for Schrödinger and Pauli operators. Pauli operators with Aharonov-Bohm magnetic field are discussed as well.

Existence Results and $$L^{\infty }$$-Bound of Solutions to Kirchhoff–Schrödinger–Hardy Type Equations Involving Double Phase Operators

Existence Results and $$L^{\infty }$$-Bound of Solutions to Kirchhoff–Schrödinger–Hardy Type Equations Involving Double Phase Operators

Some Hardy and Rellich type inequalities for affine connections

Some Hardy and Rellich type inequalities for affine connections

Hardy type inequalities with mixed weights in cones

Hardy type inequalities with mixed weights in cones

On a p(x)-biharmonic singular problem with changing sign weight and with no-flux boundary condition

In the present paper, we study $p(x)-$biharmonic problem involving $q(x)-$Hardy type potential with no-flux boundary condition. By using the mountain pass type theorem and Ekeland variatoinal principle, we obtain at least two nontrivial weak solutions.

Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type

The purpose of this paper is to establish some characterizations of mixed central Campanato space Cp→,λ(Rn), via the boundedness of the commutator operators of Hardy type. Unlike the case λ⩾0, there are some technical difficulties caused by λ<0 to be overcome. In addition, an extra assumption called as the mixed version of the reverse Hölder class be required in the proof of the converse characterization. Moreover, some further interesting conclusions for the Hardy type operators on mixed λ-central Morrey space Bp→,λ(Rn) are also derived.

Unconditional uniqueness and non-uniqueness for Hardy–Hénon parabolic equations

We study the problems of uniqueness for Hardy–Hénon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénon type) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ weighted Lorentz spaces as solution spaces. We prove unconditional uniqueness and non-uniqueness, and we establish uniqueness criterion for Hardy–Hénon parabolic equations in the weighted Lorentz spaces. The results extend the previous works on the Fujita equation and Hardy equations in Lebesgue spaces.

On weighted generator of triple sequences and its Tauberian conditions

This paper presents a new perspective on the relationship between the (N, p, q, r) method and P-convergence for triple sequences.Our primary goal is to derive Tauberian conditions that dictate the behavior of the weighted generator sequence (zlmn) in relation to the sequences (Pl), (Qm), and (Rn), with the intention of establishing a fresh interpretation. These conditions control the OL- and O-oscillatory properties and establish a connection from ( N, p, q, r) summability to P-convergence, subject to certain restrictions on the weight sequences. Furthermore, we demonstrate that specific cases, such as the OL-condition of Landau type and the O-condition of Hardy type with respect to (Pl), (Qm) and (Rn), serve as Tauberian conditions for (N, p, q, r) summability under additional conditions. Consequently, our findings encompass all the classical Tauberian theorems, including conditions related to slow decrease and slow oscillation in specific contexts.

Some uncertainty principles for the quaternion Heisenberg group

Hardy type theorem with the Heisenberg–Pauli–Weyl inequality and the logarithmic uncertainty principle for the quaternion Heisenberg group are established.

Characterizations of Composition Operators on Bloch and Hardy Type Spaces

Characterizations of Composition Operators on Bloch and Hardy Type Spaces

The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula

For a Hermitian Lie group G of tube type we find the contribution of the holomorphic discrete series to the Plancherel decomposition of the Whittaker space L2(G/N,ψ), where N is the unipotent radical of the Siegel parabolic subgroup and ψ is a certain non-degenerate unitary character on N. The holomorphic discrete series embeddings are constructed in terms of generalized Whittaker vectors for which we find explicit formulas in the bounded domain realization, the tube domain realization and the L2-model of the holomorphic discrete series. Although L2(G/N,ψ) does not have finite multiplicities in general, the holomorphic discrete series contribution does.Moreover, we obtain an explicit formula for the formal dimensions of the holomorphic discrete series embeddings, and we interpret the holomorphic discrete series contribution to L2(G/N,ψ) as boundary values of holomorphic functions on a domain Ξ in a complexification GC of G forming a Hardy type space H2(Ξ,ψ).

Hardy type identities and inequalities with divergence type operators on smooth metric measure spaces

&lt;abstract&gt;&lt;p&gt;We gave the Hardy type identities and inequalities for the divergence type operator $ L_{f, V} $ on smooth metric measure spaces. Additionally, we improved a Rellich type inequality by using the improved Hardy type inequality. Our results improved and included many previously known results as special cases.&lt;/p&gt;&lt;/abstract&gt;

Marcinkiewicz interpolation theorem for Hardy type spaces and its applications

В статье приводится ряд утверждений, подобных теореме Марцинкевича об интерполировании операторов. Отличие от классических форм этой теоремы состоит в том, что пространства суммируемых функций заменяются на некоторые классы функций, являющиеся расширениями различных пространств Харди. Указаны также некоторые приложения этих результатов: к обобщению теоремы вложения Карлесона и неравенств Харди-Литтлвуда для аналитических функций из классов Харди. Библиография: 41 название.

Some weighted dynamic inequalities of Hardy type with kernels on time scales nabla calculus

Some weighted dynamic inequalities of Hardy type with kernels on time scales nabla calculus

On Tangential Boundary Behavior of Functions from Hardy Type Spaces

On Tangential Boundary Behavior of Functions from Hardy Type Spaces

Weighted Hardy type inequalities with Robin boundary conditions

In this paper, we establish a general weighted Hardy type inequality for the $ p- $Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present some Heisenberg-Pauli-Weyl type inequalities with boundary terms on balls centred at the origin with radius $ R $ in $ \mathbb{R} ^n $.