Vector-Valued Local Approximation Spaces

被引：0

作者：

Tuomas Hytönen

Jori Merikoski

机构：

[1] University of Helsinki,Department of Mathematics and Statistics

[2] University of Turku,Department of Mathematics and Statistics

来源：

Journal of Fourier Analysis and Applications | 2019年 / 25卷

关键词：

Local approximation space; Besov space; Embedding; Uniformly convex space; Martingale cotype; Littlewood–Paley theory; Primary 46E35; Secondary 41A10; 42B25; 46B20; 60G46;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove that for every Banach space Y, the Besov spaces of functions from the n-dimensional Euclidean space to Y agree with suitable local approximation spaces with equivalent norms. In addition, we prove that the Sobolev spaces of type q are continuously embedded in the Besov spaces of the same type if and only if Y has martingale cotype q. We interpret this as an extension of earlier results of Xu (J Reine Angew Math 504:195–226, 1998), and Martínez et al. (Adv Math 203(2):430–475, 2006). These two results combined give the characterization that Y admits an equivalent norm with modulus of convexity of power type q if and only if weakly differentiable functions have good local approximations with polynomials.

引用

页码：299 / 320

页数：21

共 25 条

[1] Amann H(1997)Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications Math. Nachr. 186 5-56
[2] Bates S(1999)Affine approximation of Lipschitz functions and nonlinear quotients Geom. Funct. Anal. 9 1092-1127
[3] Johnson WB(2016)Quantitative affine approximation for UMD targets Discrete Anal. 1 37-252
[4] Lindenstrauss J(2008)Embedding vector-valued Besov spaces into spaces of Math. Nachr. 281 238-388
[5] Preiss D(2005)-radonifying operators J. Funct. Anal. 227 372-475
[6] Schechtman G(2006)Refined limiting imbeddings for Sobolev spaces of vector-valued functions Adv. Math. 203 430-136
[7] Hytönen T(2015)Vector-valued Littlewood–Paley–Stein theory for semigroups J. Fourier Anal. Appl. 21 95-350
[8] Li S(1975)Pointwise multiplication on vector-valued function spaces with power weights Israel J. Math. 20 326-1106
[9] Naor A(2012)Martingales with values in uniformly convex spaces Math. Nachr. 285 1082-226
[10] Kalton N(1998)Traces of vector-valued Sobolev spaces J. Reine Angew. Math. 504 195-undefined

← 1 2 3 →