Optimality conditions for change of variable operators in Sobolev spaces with mixed derivatives

IF 0.5 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2026-02-23 DOI:10.1007/s10476-026-00141-9

V. K. Nguyen

引用次数: 0

Abstract

Change of variable plays an important role in constructing sparse grids for multivariate numerical integration of functions on \([0,1]^d\). This is a modification of cubature formulae for functions supported in \([0,1]^d\) which yields the same order of convergence. In this paper we prove the necessary and sufficient conditions for the continuity of the change of variable operator in the Sobolev space with mixed derivatives \(\boldsymbol{W}_p^m (\mathbb{R}^d)\) with \(1\leq p<\infty\) . The result is then extended to the spaces on the unit cube \(\boldsymbol{W}_p^m([0,1]^d)\).

查看原文本刊更多论文

具有混合导数的Sobolev空间中变量算子变化的最优性条件

在\([0,1]^d\)上建立多元函数数值积分的稀疏网格时，变量的变化起着重要的作用。这是对\([0,1]^d\)中支持的函数的培养公式的修改，它产生相同的收敛阶。本文用\(1\leq p<\infty\)证明了Sobolev空间中具有混合导数\(\boldsymbol{W}_p^m (\mathbb{R}^d)\)的变量算子变化连续性的充分必要条件。然后将结果扩展到单位立方体\(\boldsymbol{W}_p^m([0,1]^d)\)上的空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.