Exact Jackson Inequalities And Widths Of Differentiable Function Class In Weighted L₂ Space With Two Variables

In this paper,we mainly study the best approximation of differentiable function class on bivariate weighted L₂space by algebraic polynomials.Firstly,on the L₂space with Laguerre weight of two variables,we study the Jackson inequality approximated by polynomials for the class of differentiable functions,and use the obtained results to study the problem of width on this space,and obtain the exact results of Jackson inequality and width.Then,we study the approximation problem on the L₂space with Hermite weight of two variables,and obtain the corresponding exact conclusions of Jackson inequality and width.