左拟中插式Gamma算子在Orlicz空间中的逼近性质

为了得到更快的逼近速度,人们开始研究算子的拟中插式的逼近性质.在Orlicz空间中讨论左拟中插式Gamma算子的逼近性质,利用了Ditzian-Totik模与K-泛函的等价性、Holder不等式、Cauchy-Schwarz不等式和Laguerre多项式等等工具得到了逼近的正、逆和等价定理,推广了左拟中插式Gamma算子在L_p空间中的逼近结果,改进了Gamma算子在Orlicz空间的逼近性质.     

积分型Hermite-Fejér与Lagrange插值算子在Orlicz空间内的逼近

构造了一类积分型Hermite-Fejér插值和两类积分型Lagrange插值,在构造性方法的基础上,利用函数逼近论中的常用方法和技巧,以及连续模、H■lder不等式、Hardy-Littlewood极大函数等工具,得到三类插值在Orlicz空间内的逼近定理。     

Gauss-Weierstrass算子在Orlicz空间内的加Jacobi权逼近

讨论Gauss-Weierstrass算子加Jacobi权在Orlicz空间内的逼近度,应用Hol der不等式、Jensen不等式、Hardy-Littlewood极大函数以及Orlicz空间中K-泛函和光滑模的等价性证明了该算子的逼近性质。     

An Approximation by Reciprocals of Polynomials with Positive Coefficients in Orlicz Spaces

对于连续函数用多项式倒数逼近的问题,在连续函数空间和Lp(p≥1)空间中已有许多研究,而在Orlicz空间中这类问题研究的相对少一些,为此利用不等式技巧与K泛函等工具在Orlicz空间内研究了正系数多项式倒数逼近的问题,得到了逼近阶的一种估计.     

Orlicz空间中正系数多项式倒数逼近

对于连续函数用多项式倒数逼近的问题,在连续函数空间和Lp(p1)空间中已有许多研究,而在Orlicz空间中这类问题研究的相对少一些,为此利用不等式技巧与K泛函等工具在Orlicz空间内研究了正系数多项式倒数逼近的问题,得到了逼近阶的一种估计.     

Sz■sz-Mirakjan-Durrmeyer算子线性组合的加权Orlicz逼近

讨论Sz■sz-Mirakjan-Durrmeyer算子的线性组合在Orlicz空间内的逼近问题,借助H?lder不等式、K-泛函、Hardy不等式、光滑模等工具,给出Sz■sz-Mirakjan-Durrmeyer算子的线性组合在Orlicz空间内Jacobi加权的逼近定理。     

Gamma算子在Orlicz空间内的逼近

利用Taylor公式,Hardy-Littlewood极大函数和Jensen不等式等工具研究了Gamma算子在Orlicz空间内的逼近问题,得出了逼近阶及其逼近等价定理.     

An Approximation for Gamma Operators in Orlicz Spaces

利用Taylor公式,Hardy-Littlewood极大函数和Jensen不等式等工具研究了Gamma算子在Orlicz空间内的逼近问题,得出了逼近阶及其逼近等价定理.     

样条子空间逼近周期可微函数的最佳逼近度

样条函数类与周期函数类的逼近问题是函数逼近论的重要内容。为了在较大范围内研究最佳逼近问题,在Lp空间内研究最佳逼近方法的基础上,利用最佳逼近的对偶原理、Holder不等式等工具,借助抽象逼近的方法和技巧,研究了样条子空间在Orlicz空间内的最佳逼近问题,给出了最佳逼近度的估计式。研究结果对误差估计、精度分析可提供必要的理论分析依据和参考数据。     

Lupas-Baskakov型算子在Orlicz空间内的逼近

利用函数逼近论中的常用方法和技巧以及Ditzian-Totik光滑模、K-泛函、凸函数的Jensen不等式、Hardy-Littlewood极大函数等工具研究了Lupas-Baskakov型算子在Orlicz空间内逼近的正逆定理.     

Dual Orlicz affine surface area

According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.     

On reverses of the <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-Busemann-Petty centroid inequality and its applications

In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.     

Characterizations of <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>(<Emphasis Type="Italic">R</Emphasis>) using tight wavelet frames

In this paper,a Littlewood-Paley function characterization of the spaces L p(R),1相似文献   

Weighted inequalities in martingale spaces

We give a condition on the couple of weights(u,v) for Doob's operator to be a bounded one from martingale space Lp(u) to function space Lp(v) .Moreover,we also obtain necessary and sufficient conditions in order that the maximal geometric mean operator is bounded from martingale space Lp(u) to function space Lp(v) or Lp,∞(v) .     

对偶L_q变换法则

在已有结果的基础上对对偶L_q Brunn-Minkowski理论做了一些推广,主要讨论了对偶L_q Brunn-Minkowski型不等式并得到部分结果.给出统一的处理对偶L_q Brunn-Minkowski型不等式的方法,称此方法为对偶L_q变换法则,通过运用此法则给出了关于对偶混合体积著名的对偶L_q Brunn-Minkowski型不等式的简化证明.     

Musielak-Orlicz序列空间的WNUS性质

对赋Luxemburg范数的Orlicz序列空间和Cesaro空间(这里ces_p,(1＜p＜∞))的系数R(X)进行了计算,给出了具有R(X)＜2性质的非自反Banach空间X的例子.指明了弱近一致光滑性质强于不等式R(X)＜2.     

Petty projection inequalities for the general L p -mixed projection bodies

In this paper,the definition of the general L p-mixed projection bodies is introduced,and the general L p-projection bodies given by Ludwig is a special case for the general L p-mixed projection bodies.Then the Petty projection inequality for the general L p-mixed projection bodies is shown.Moreover,the monotonicity for the general L p-mixed projection bodies is obtained.     

An extrapolation theorem on martingale spaces with Ap weights

In this paper, we prove an extrapolation theorem of operators in martingale spaces with A _p weights, which shows that for operators T defined on martingale space L _u ¹ , if T is bounded on martingale space L ^p0(w) for some 1 < p ₀ < ∞ and every, w∈ A _∞, so it is on L ^p,s (w) for every 1 < p, s < ∞, and w ∈ A _∞. We also get some properties of A _p weights and prove that if w ∈ A ₁, then the maximal operator M is bounded on L ^p,q (w) with 1 < p < ∞, 1 < q ≤ ∞.     

B-Valued Dyadic Derivative

The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.