Boundedness of Product Type Pseudodifferential Operators on Spaces of Besov Type

In this paper we consider pseudodifferential operators associated with symbols satisfying estimates of product type, and give some sufficient conditions for the operators to be bounded on BESOV spaces and on TRIEBEL —LIZORKIN spaces of product type corresponding to the above estimates. In the proof we use the characterization of these spaces by approximation by entire functions.     

Certain Norm Related Quantities of Unbounded Linear Operators

Certain norm related functions of linear operators are considered in the very general setting of not necessarily continuous linear operators in normed spaces. These are shown to be closely related to the theory of precompact, strictly cosingular and a class of Φ_? type operators in addition to having applications to perturbation theory. We also obtain some basic continuity and precompactness properties of linear operators in normed spaces which are expressed in terms of the functions under consideration.     

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.     

Weighted Approximation of Functions by Meyer–König and Zeller Operators of Max-Product Type

In this paper, we study the uniform approximation of functions by Meyer–König and Zeller operators of max-product type in some weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity.     

Local operators between spaces of ultradifferentiable functions and ultradistributions

In this article we characterize certain ultradifferential operators by the condition of being local. First, we examine the continuity properties of local linear operators on spaces of ultradifferentiable functions in the sense of Beurling and of Roumieu. Next, a structure theorem for vector-valued ultradistributions with support at the origin is proved. This result leads to a representation theorem for continuous local operators from spaces of ultradifferentiable functions into various spaces of ultradistributions. In combination with the continuity results we thus obtain in many cases the desired characterization.     

A unified framework for the discretization of nonlinear operator equations

A general theory for the discretization of non-linear operator equations is presented. A given operator with certain continuity and compactness properties is approximated by a sequence of operators acting in different spaces, usually finite dimensional. Connection maps, such as restriction and interpolation, relate the spaces. The abstract convergence theory is formulated in terms of metric spaces. Specializations and applications to differential and integral equations involve normed linear spaces. The case with the same setting for the original and approximate problems was treated in [1]. For typical problems, both types of discretization methods are available. They are related by means of the connection maps.     

Reconstruction of Baskakov operators preserving some exponential functions

The present paper deals with a new modification of Baskakov operators in which the functions exp(μt) and exp(2μt), μ>0 are preserved. Approximation properties of the operators are captured, ie, uniform convergence and rate of convergence of the operators in terms of modulus of continuity, approximation behaviors of the operators exponential weighted spaces, and pointwise convergence of the operators by means of the Voronovskaya theorem. Advantages of the operators for some special functions are presented.     

Truncations of multilinear Hankel operators

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

     

次范整线性空间上的可加奇性算子

研究次范整线性空间上的可加奇性算子理论.引进可加奇性算子的三种不同的次范数和拟次范数,利用它们刻画可加奇性算子的三种有界性:有界、局部有界和球有界,深入讨论这三种有界性之间的关系,以及它们与连续性的关系.同时,还进一步研究次范整线性空间上连续可加奇性算子族的共鸣定理.     

Functions of the first Baire class with values in metric spaces and some applications of them

The classical Baire characterization of functions of the first Baire class in terms of points of continuity is carried over to functions with values in certain metric spaces. As corollaries we get new characterizations of Radon-Nikodym operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 135–149, 1984.     

Differential equations on manifolds with edge singularities in spaces with asymptotics

The present paper deals with differential equations with edge degeneration in spaces with asymptotics. We give the definition of an edge space with asymptotics, prove the continuity of operators with edge degeneration in the scale of these spaces, present statements of problems with edge operators, and state conditions providing their Fredholm property.     

Automatic continuity of generalized local linear operators

In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.     

Spectrum and Singular Integrals on a New Weighted Function Space

We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderón–Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions.     

Composition operators on Bloch-Orlicz type spaces

In this paper we use Young’s functions to define the Bloch-Orlicz spaces as a generalization of Bloch spaces. We study continuity, boundedness from below and compactness of composition operators on Bloch-Orlicz spaces.     

The Continuity of Commutators on Triebel-Lizorkin Spaces

The purpose of this paper is to study the continuity in the context of Triebel-Lizorkin spaces for some commutators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral and Bochner-Riesz operator.     

L-fuzzy层保序算子空间

在L拓扑空间中引入层保序算子、层连续等概念,讨论他们的基本性质,给出了它们的特征性质刻画。说明了可拓扑生成的层保序算子拓扑空间与一般拓扑中的保序算子空间之间的关系。     

Estimation of the uniform modulus of continuity of the generalized Bessel potential

We study generalized Bessel potentials constructed by means of convolutions of functions with kernels that generalize the classical Bessel-Macdonald kernels. In contrast to the classical case, nonpower singularities of kernels in a neighborhood of the origin are admitted. The integral properties of functions are characterized in terms of decreasing rearrangements. The differential properties of potentials are described by the kth-order moduli of continuity in the uniform norm. An order-sharp upper estimate is established for the modulus of continuity of a potential. Such estimates play an important role in the theory of function spaces. They allow one to establish sharp embedding theorems for potentials, find majorants of the moduli of continuity, and estimate the approximation numbers of embedding operators.     

Zygmund-type estimates for fractional integration and differentiation operators of variable order

We consider non-standard generalized Hölder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Hölder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant.     

General Function Spaces,V. (The Spaces B and F: The Case 0<p≦∞)

In this paper quasi-BANACH spaces of (generalized) distributions are considered, including spaces of BESOV type, HARDY type and SOBOLEV type. The methods are based on the real variable approach to the HARDY spaces by FEFFERMAN and STEIN, and on the modification of this approach in connection with spaces of F-type by PEETRE.     

Isotone cones in Banach spaces and applications to best approximations of operators without continuity conditions

In this paper, we introduce the concept of isotone cones in Banach spaces. Then, we apply the order monotonic property of the metric projection operator to prove the existence of best approximations for some operators without continuity conditions in partially ordered Banach spaces.