BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR

Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed

CONTINUITY FOR MAXIMAL COMMUTATORS OF BOCHNER-RIESZ OPERATORS WITH BMO FUNCTIONS

Let p is an element of (n/(n + 1), 1]. The authors investigate the (H-b(p)(R-n), L-p(R-n))-type and (H-b(p,infinity)(R-n), L-p,L-infinity(R-n))-type continuities for the maximal operators associated with the commutators of Bochner-Riesz operators with BMO(R-n) functions, where H-b(p)(R-n) and H-b(p,infinity)(R-n) are, respectively, the variants of the standard Hardy spaces and the standard weak Hardy spaces.

Boundedness for Maximal Bochner-Riesz Operator and Commutator on Generalized Morrey Space

In this paper,we have obtained the boundedness of maximal Bochner-Riesz operator on generalized Morrey space.Also,it is right for its commutator.

COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(R^n) function and T~α.

COMMUTATORS OF BOCHNER-RIESZ OPERATORS FOR A CLASS OF RADIAL FUNCTIONS

In this article, we prove the boundedness of commutators generated by BochnerRiesz operators below the critical index and BMO functions on the class of radial functions in Lp（Rn） with ｜1/p-1/2｜〈（1＋2α）/（2n）.

THE BOUNDEDNESS OF MAXIMAL BOCHNER-RIESZ OPERATOR AND MAXIMAL COMMUTATOR ON MORREY TYPE SPACES

The boundedness of maximal Bochner-Riesz operator B^δ＊ and that of maximal commutator B^bδ＊, generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are established.

Weighted Lipschitz Estimate for Commutator of Bochner-Riesz Operators on Weighted Morrey Spaces

In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

The construction and approximation of some neural networks operators

In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.

POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.

WEIGHTED BOUNDEDNESS OF A ROUGH MAXIMAL OPERATOR

In this note the authors give the weighted Lp-boundedness for a class of maximal singular integral operators with rough kernel. The result in this note is an improvement and extension of the result obtained by Chen and Lin in 1990.

TWO GENERALIZATIONS OF HARDY-LITTLEWOOD MAXIMAL OPERATOR

Two generalizations of Hardy-Littlewood maximal operator are considered. Some estimates for them are obtained.

Multilinear Commutators of Sublinear Operators on Triebel-Lizorkin Spaces

In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.

A New Estimate for Bochner–Riesz Operators at the Critical Index on Weighted Hardy Spaces

Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） to the weighted weak Hardy spaces WHwp （Rn） for 0 〈 p 〈 1 and δ = n/p- （n ＋ 1）/2. This result is new even in the unweighted case.

Certain averaging operators on Triebel-Lizorkin spaces

In this article,we study the boundedness properties of the averaging operator S_(t)^(γ) on Triebel-Lizorkin spaces F_(p,q)^(α)(R^(n))for various p,q.As an application,we obtain the norm convergence rate for S_(t)^(γ)(f)on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S_(t)^(γ) is given.

Angular Momentun Eigenfunctions in Ultraspherical Space

After a series of transformation^([1,2])if the interaction is supercentral,the Schrodinger equation in the ultra spherical frame

SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIFFORD ANALYSIS

New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein.

Spherical uncertain linguistic Hamacher aggregation operators and their application on achieving consistent opinion fusion in group decision making

Purpose-The aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers(SULNs).Design/methodology/approach-First,the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs.Furthermore,the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.Findings-The authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.Originality/value-In order to give an application of the introduced operators,the authors first constrict a system of multi-attribute decision-making algorithm.

椭球型Bochner-Riesz平均的L^p收敛

在本文中,我们刻画了椭球型Bochner-Riesz平均Lp收敛性与Lp有界性的关系.我们也证明了在适当的指标下,椭球型Bochner-Riesz平均的Lp收敛性.