We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multipl...We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.展开更多
Suppose that a continuous 2re-periodic function f on the real axis changes its monotonicity at points Yi In this paper, for each n _ N, a trigonometric polynomial Pn of order cn is found such that： Pn has the same ...Suppose that a continuous 2re-periodic function f on the real axis changes its monotonicity at points Yi In this paper, for each n _ N, a trigonometric polynomial Pn of order cn is found such that： Pn has the same monotonicity as f, everywhere except, perhaps, the small intervals.展开更多
On the basis of Part (Ⅰ) of this series some applications to the approximation of set_valued functions are obtained: Korovkin type theorems, a method to extend classical approximation operators to the set_valued sett...On the basis of Part (Ⅰ) of this series some applications to the approximation of set_valued functions are obtained: Korovkin type theorems, a method to extend classical approximation operators to the set_valued setting and a Jackson type estimate.展开更多
This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means...This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality.展开更多
基金supported by Key Academic Discipline of Zhejiang Province of China and National NaturalScience Foundation of China (Grant Nos. 10571014, 10631080, 10671019)
文摘We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.
文摘Suppose that a continuous 2re-periodic function f on the real axis changes its monotonicity at points Yi In this paper, for each n _ N, a trigonometric polynomial Pn of order cn is found such that： Pn has the same monotonicity as f, everywhere except, perhaps, the small intervals.
文摘On the basis of Part (Ⅰ) of this series some applications to the approximation of set_valued functions are obtained: Korovkin type theorems, a method to extend classical approximation operators to the set_valued setting and a Jackson type estimate.
基金Supported partially by the NSF(61877039)the NSFC/RGC Joint Research Scheme of China(12061160462 and N_CityU102/20)the NSF of Zhejiang Province(LY19F020013)。
基金Supported by the National Natural Science Foundation of China（liT61055） Supported by the Inner Mongolia Autonomous Region Natural Science Foundation of China（2017MS0123）
文摘This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality.
