标题： 最大乘积Kantorovich采样算子：函数空间中的定量估计 显示英文标题

标题： Max-product Kantorovich sampling operators: quantitative estimates in functional spaces

摘要： 在本文中，我们研究了基于广义核在Orlicz空间设置中的最大-乘积Kantorovich采样算子的逼近阶。我们使用Orlicz型光滑模为所考虑的采样型算子族建立了定量估计，该估计涉及空间的模函数。从这个结果中，当考虑属于适当Lipschitz类的函数时，可以得到收敛的定性阶。另一方面，在紧致情况下，我们利用Orlicz空间中K-泛函的合适定义，以提供所涉及算子的逼近误差的上界。在Orlicz空间的一般框架下的处理使得能够获得关于收敛速率的统一理论，因为所证明的结果可以推导出广泛的函数空间，如$L^{p}$-空间、插值空间和指数空间。 显示英文摘要

摘要： In this paper, we study the order of approximation for max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. We establish a quantitative estimate for the considered family of sampling-type operators using the Orlicz-type modulus of smoothness, which involves the modular functional of the space. From this result, it is possible to obtain the qualitative order of convergence when functions belonging to suitable Lipschitz classes are considered. On the other hand, in the compact case, we exploit a suitable definition of K-functional in Orlicz spaces in order to provide an upper bound for the approximation error of the involved operators. The treatment in the general framework of Orlicz spaces allows one to obtain a unifying theory on the rate of convergence, as the proved results can be deduced for a wide range of functional spaces, such as $L^{p}$-spaces, interpolation spaces and exponential spaces.