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### A class of integral operators on mixed norm spaces in the unit ball

Czechoslovak Mathematical Journal

This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.

### A class of pairs of weights related to the boundedness of the Fractional Integral Operator between ${L}^{p}$ and Lipschitz spaces

Commentationes Mathematicae Universitatis Carolinae

In [P] we characterize the pairs of weights for which the fractional integral operator ${I}_{\gamma }$ of order $\gamma$ from a weighted Lebesgue space into a suitable weighted $BMO$ and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of ${I}_{\gamma }$ acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...

### A continuity in the weak topologies of a vector integral operator.

Collectanea Mathematica

### A modular convergence theorem for certain nonlinear integral operators with homogeneous kernel.

Collectanea Mathematica

### A new approach to nonlinear singular integral operators depending on three parameters

Open Mathematics

In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , ${T}_{\lambda }\left(f;x,y\right)=\underset{{ℝ}^{2}}{\phantom{\rule{0.277778em}{0ex}}\int \int \phantom{\rule{0.277778em}{0ex}}}\left(t-x,s-y,f\left(t,s\right)\right)dsdt,\phantom{\rule{0.277778em}{0ex}}\left(x,y\right)\in {ℝ}^{2},\lambda \in \Lambda ,$ where Λ is a set of non-negative numbers with accumulation point λ0.

### A new general integral operator defined by Al-Oboudi differential operator.

Journal of Inequalities and Applications [electronic only]

### A note on generalized fractional integral operators on generalized Morrey spaces.

Boundary Value Problems [electronic only]

### A probabilistic approach to the boundedness of singular integral operators

Séminaire de probabilités de Strasbourg

### A rearrangement estimate for the generalized multilinear fractional integrals.

Sibirskij Matematicheskij Zhurnal

### A sharp rearrangement inequality for the fractional maximal operator

Studia Mathematica

We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, ${M}_{\gamma }⨍$, by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of ${M}_{\gamma }$ between classical Lorentz spaces.

### A spectral mapping theorem for evolution semigroups on asymptotically almost periodic functions defined on the half line.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A uniform estimate for quartile operators.

Revista Matemática Iberoamericana

There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove Lp estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model...

### A weighted estimate for an intermediate operator on the cone of nonnegative functions.

Sibirskij Matematicheskij Zhurnal

### A weighted inequality for the Hardy operator involving suprema

Commentationes Mathematicae Universitatis Carolinae

Let $u$ be a weight on $\left(0,\infty \right)$. Assume that $u$ is continuous on $\left(0,\infty \right)$. Let the operator ${S}_{u}$ be given at measurable non-negative function $\varphi$ on $\left(0,\infty \right)$ by ${S}_{u}\varphi \left(t\right)=\underset{0<\tau \le t}{sup}u\left(\tau \right)\varphi \left(\tau \right).$ We characterize weights $v,w$ on $\left(0,\infty \right)$ for which there exists a positive constant $C$ such that the inequality ${\left({\int }_{0}^{\infty }{\left[{S}_{u}\varphi \left(t\right)\right]}^{q}w\left(t\right)\phantom{\rule{0.166667em}{0ex}}dt\right)}^{\frac{1}{q}}\lesssim {\left({\int }_{0}^{\infty }{\left[\varphi \left(t\right)\right]}^{p}v\left(t\right)\phantom{\rule{0.166667em}{0ex}}dt\right)}^{\frac{1}{p}}$ holds for every $0. Such inequalities have been used in the study of optimal Sobolev embeddings and boundedness of certain operators on classical Lorenz spaces.

### Abschätzungen für den zweiten Eigenwert eines positiven Operators.

Aequationes mathematicae

### Alternative characterisations of Lorentz-Karamata spaces

Czechoslovak Mathematical Journal

We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.

### An integral operator inequality with applications.

Journal of Inequalities and Applications [electronic only]

### An integral operator representation of classical periodic pseudodifferential operators.

Zeitschrift für Analysis und ihre Anwendungen

### Applications of the spectral radius to some integral equations

Commentationes Mathematicae Universitatis Carolinae

In the paper  we proved a fixed point theorem for an operator $𝒜$, which satisfies a generalized Lipschitz condition with respect to a linear bounded operator $A$, that is: $m\left(𝒜x-𝒜y\right)\prec Am\left(x-y\right).$ The purpose of this paper is to show that the results obtained in ,  can be extended to a nonlinear operator $A$.

### Approximation results for nonlinear integral operators in modular spaces and applications

Annales Polonici Mathematici

We obtain modular convergence theorems in modular spaces for nets of operators of the form $\left({T}_{w}f\right)\left(s\right)={\int }_{H}{K}_{w}\left(s-{h}_{w}\left(t\right),f\left({h}_{w}\left(t\right)\right)\right)d{\mu }_{H}\left(t\right)$, w > 0, s ∈ G, where G and H are topological groups and ${{h}_{w}}_{w>0}$ is a family of homeomorphisms ${h}_{w}:H\to {h}_{w}\left(H\right)\subset G.$ Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

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