COMPLEX INTERPOLATION OF L_(p)(C,H)SPACES WITH RESPECT TO CULLEN-REGULAR

The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).

COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJR POINTS ON A CURVE

The results of accurate order of uniform approximation and simultaneous approximation in the early work ＂Jackson Type Theorems on Complex Curves＂ are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈（f,z） with disturbed sample values f（z^＊） ＋ Sk are also proved in this article.

Complex Interpolation of Weighted Besov and Lizorkin–Triebel Spaces

We study complex interpolation of weighted Besov and Lizorkin–Triebel spaces.The used weights w0,w1 are local Muckenhoupt weights in the sense of Rychkov.As a first step we calculate the Calder′on products of associated sequence spaces.Finally,as a corollary of these investigations,we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin–Triebel spaces on Rd.

Complex interpolation of various subspaces of Morrey spaces

In this article,we discuss the complex interpolation of various closed subspaces of Morrey spaces.We have been considering some closed subspaces of Morrey spaces in our earlier works.The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al.(2015),it seems to be natural to consider the convolution property as well.Our result will extend the results by Hakim and Sawano(2017)and Hakim et al.(2017).

Complex interpolation and Calderon product of quasi-Banach spaces

We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderon product. This generalizes a classical result by V. A. Shestakov in 1974 for Banach lattices.

THE BERNSTEIN TYPE INEQUALITY AND SIMULTANEOUS APPROXIMATION BY INTERPOLATION POLYNOMIALS IN COMPLEX DOMAIN

In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.

INTERPOLATION ON THE COMPLEX HILBERT SPHERE

Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a function in the linear span of the l functionswhen is a suitable function that operates on nonnegative definite matrices.Conditions for the strict positive definiteness of the kernel are obtained.

Function spaces of Besov-type and Triebel-Lizorkin-type——a survey

This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.

L^p MIXED-NORM ESTIMATES FOR CONVOLUTION OPERATOR DEFINED BY SINGULAR MEASURES

Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.

Inequalities for Higher Order Riesz-Laguerre Transforms

The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L1 (wdμα) into L1,∞ (dμα), under specific value α, where μα is the Laguerre measure.

Complex matrix interpolation model of the S-transform for electric load movement forecast

Electric load movement forecast is increasingly importance for the industry.This study addresses the load movement forecast modeling based on complex matrix interpolation of the S-transform(ST).In complex matrix of time-frequency representation of the ST,each row follows conjugate symmetric property and each column appears a certain degree of similarity.Based on these characteristics,a complex matrix interpolation method for the time-frequency representation of the ST is proposed to interpolate each row of the complex matrix based on the conjugate symmetric property,and then to perform nearestneighbor interpolation on each column.Then with periodic extension for daily and yearly electric load movement,a forecast model employing the complex matrix interpolation of the ST is introduced.The forecast approach is applied to predict daily load movement of the European Network on Intelligent Technologies(EUNITE)load dataset and annual electric load movement of State Gird Corporation of China and its branches in 2005 and 2006.Result analysis indicates workability and effectiveness of the proposed method.

Linear Combinations of Composition Operators on Weighted Dirichlet Spaces

In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.