Generalized composition and Volterra type operators between QK spaces

Abstract

In this paper, the boundedness and compactness of the generalized composition operators and the products of Volterra type operators a nd composition operators between Q_K spaces are investigated. We also give a necessary condition for multiplication operators between Q_K spaces to be bounded or compact.     

Littlewood–Paley decomposition in quantum calculus

ABSTRACT

We introduce Littlewood–Paley decomposition related to q-Rubin's operator, this allows us to provide a dyadic characterization of Sobolev, Hölder and Lebesgue spaces associated with the q-Rubin's operators and to establish some embedding results for these spaces. We construct the paraproduct operators associated with the q-Rubin's operators and we establish its action on the Sobolev and Hölder spaces.     

THE QUASI-GEOSTROPHIC EQUATION AND ITS TWO REGULARIZATIONS

Abstract

A symbolic calculus for the transposes of a class of bilinear pseudodifferential operators is developed. The calculus is used to obtain boundedness results on products of Lebesgue spaces. A larger class of pseudodifferential operators that does not admit a calculus is also considered. Such a class is the bilinear analog of the so-called exotic class of linear pseudodifferential operators and fail to produce bounded operators on products of Lebesgue spaces. Nevertheless, the operators are shown to be bounded on products of Sobolev spaces with positive smoothness, generalizing the Leibniz rule estimates for products of functions.     

r-ASYMPTOTICALLY QUASI-FINITE RANK OPERATORS AND THE SPECTRUM OF MEASURES

Abstract

The r-asymptotically quasi finite rank operators were introduced in [10]. For regular operators on Banach lattices, these operators are the order theoretic analogue of Riesz operators on Banach spaces. We establish their basic properties and apply these in the spectral analysis of convolution operators.     

Difference of Differentiation Composition Operators on the Fractional Cauchy Transforms Spaces

Abstract

In this paper, we consider the boundedness and compactness of the differences of differentiation composition operators from the space of fractional Cauchy transforms to the Bloch-type spaces and the weighted Dirichlet spaces. Surprisingly, these characterizations are free from pseudo-hyperbolic metric, which is a common feature of all the preceding characterizations of difference of differentiation composition operators on various spaces of holomorphic functions.     

Anti-Wick Symbols for Infinite Products in K-Homology

We consider infinite products in K-homology. We study these products in relation with operators on filtered Hilbert spaces, and infinite iterations of universal constructions on C*-algebras. In particular, infinite tensor power of extensions of pseudodifferential operators on R are considered. We extend anti-Wick pseudodifferential operators to infinite tensor products of spaces of the type L ²(R), and compare our infinite tensor power construction with an extension of pseudodifferential operators on R . We show that the K-theory connecting maps coincide. We propose a natural definition of ellipticity for anti-Wick operators on R, compute the corresponding index, and draw some consequences concerning these operators.     

Spaces of Ideal Convergent Sequences of Bounded Linear Operators

Abstract

The notation of I–convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I–convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces.     

Strong inclusion orders between L-subsets and its applications in L-convex spaces

Abstract

In this paper, the concept of strong inclusion orders between L-subsets is introduced. As a tool, it is applied to the following aspects. Firstly, the notion of algebraic L-closure operators is proposed and the resulting category is shown to be isomorphic to the category of L-convex spaces (also called algebraic L-closure spaces). Secondly, restricted L-hull operators, as generalizations of restricted hull operators, are introduced and the resulting category is also proved to be isomorphic to the category of L-convex spaces. Finally, by using the properties of strong inclusion orders, it is shown that the category of convex spaces can be embedded in the category of stratified L-convex spaces as a reflective subcategory and the concrete form of the coreflective functor from the category of L-convex spaces to the category of stratified L-convex spaces is presented.     

The Root Problem For Stochastic Operators

Abstract

This note contains an order-theoretical approach to the theory of stochastic operators. Our main result is a necessary condition for the existence of n-th roots of an ergodic and conservative operator, which generalizes known results for measure-preserving operators and operators on L ^p-type spaces.     

Boundedness of Calderón-Zygmund operators in product Hardy spaces

By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.     

Singular integrals and commutators on homogeneous groups

Let G be a homogeneous group. In this paper, the authors establish several general theorems for the boundedness of sublinear operators and commutators generated by linear operators and BMO(G)functions on the weighted Lebesgue space on G. The conditions of these theorems are satisfied by many important operators in analysis and these operators satisfy only some weak conditions on the size of operators and are known to be bounded in the unweighted case. Some of these theorems are best possible even when G is the Euclidean space. The authors also give some applications of their theorems to the boundedness on weighted spaces of rough singular integrals, oscillatory integrals, parabolic singular integrals, their commutators and the maximal operators associated with them.     

PROJECTIONS ON OPERATOR DUALS

Abstract

We discuss the existence of a projection with kernel K_b(E,F) ¹ (the annihilator of the quasi-compact operators) on the dual space of the space L _b,(E, F) of continous linear operators. Our results are proved in the context of Hausdorff locally convex spaces, but also provide extensions of recent results in the context of Banach spaces.     

Error Estimate of Data Dependence for Discontinuous Operators by New Iteration Process with Convergence Analysis

Abstract

In this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results.     

Measures of Non-compactness of Operators on Banach Lattices

[Indag. Math.(N.S.) 2(2) (1991), 149–158; Uspehi Mat. Nauk 27(1(163)) (1972), 81–146] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of [J. Funct. Anal. 78(1) (1988), 31–55] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness.     

Boundedness of Monge–Ampère singular integral operators on Besov spaces

ABSTRACT

The purpose of this paper is to establish a theory of Besov spaces associated with sections under only the doubling condition on the measure and prove that Monge–Ampère singular integral operators are bounded on these spaces.     

Superposition operators between weighted spaces of analytic functions

Abstract

We study the existence and the continuity of superposition operators between weighted spaces of holomorphic functions in terms of the weights.     

A CHARACTERIZATION OF LINEAR OPERATORS IN CERTAIN PARANORMED SEQUENCE SPACES

Abstract

We define a new class B of sets of strongly summable and bounded sequences, determine their first and second α- and β-duals, and characterize linear operators on the spaces in B.     

The maximal conjugate and Hilbert operators on real Hardy spaces

Summary We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H¹ to L¹, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T² and R².     

Toeplitz Type Operators on the Hardy-Orlicz Space

In this article, we consider Toeplitz type operators and Hankel type operators in the Hardy-Orlicz space H_φ (Ω) and find a condition for the symbol so that they behave well on H_φ (Ω). Furthermore, we will show that Gleason's problem is solved affirmatively in some Hardy-Orlicz spaces.     

EQUIMEASURABLE SETS IN RIESZ SPACES

Abstract

We discuss the notion of equimeasurability in the general setting of Riesz spaces and obtain a characterization for (Carleman) abstract kernel operators in terms of equimea=surable sets.