Anisotropic Local Hardy Spaces

Abstract

In this paper we introduce and study the anisotropic local Hardy spaces h p A (R n ) 0 < p ≤ 1, associated with the expansive matrix A. We obtain an atomic characterization of the distributions in h p A (R n ). Also we describe the dual spaces of our local Hardy anisotropic spaces as anisotropic Campanato type spaces.

Real‐variable characterizations of local Hardy spaces on spaces of homogeneous type

“…Also, note that the anisotropic Euclidean space is a special space of homogeneous type. Thus, our results cover the results in [2] when . Moreover, compared with the results in [2], ours also contain the Littlewood–Paley function and finite atomic characterizations of local Hardy spaces.…”

“…[40] introduced the local Hardy type spaces built on ball quasi‐Banach spaces. On another hand, Betancor and Damián [2] introduced the anisotropic local Hardy spaces, whose underlying space is more likely to be a space of homogeneous type.…”

Estimates for multilinear operators on anisotropic function spaces and their applications

“…考虑到各向异性 Hardy 空间 H p A (R n ) 的一般性, 更多各向异性 Hardy 空间 H p A (R n ) 的实变特征及其应用已被研究 (参 见文献 [1,[9][10][11]). 另外, 局部各向异性 Hardy 空间 [12] 、各向异性 Hardy Lorentz 空间 [13] 和各向异性 Musielak-Orlicz Hardy 空间 [14] 等都已被研究. 当研究起源于小波理论的一般离散扩张结构时, 各向异 性函数空间也扮演着重要的角色 (参见文献 [1]).…”

A Survey on Some Anisotropic Hardy-Type Function Spaces

“…Moreover, Barrios et al [4] further characterized the anisotropic Besov spaces in terms of Peetre maximal functions and approximations; Li et al [64] presented the duality theory of weighted anisotropic Besov and Triebel-Lizorkin spaces; Li et al [65] and Liu et al [80,81] established the characterizations of weighted anisotropic Besov and Triebel-Lizorkin spaces via Littlewood-Paley functions involving ball averages. In addition, anisotropic weak Hardy spaces were studied by Ding et al [27] and Barrios et al [5], which were just special cases of anisotropic Hardy-Lorentz spaces introduced by Liu et al in [77,79]; anisotropic local Hardy spaces were investigated by Betancor et al [11]; weighted anisotropic product Hardy spaces were considered by Bownik et al [17] and Li et al [63]. In 2014, based on the work of both Bownik [12] and Ky [60], Li et al [68] introduced the anisotropic Musielak-Orlicz Hardy space, which was a generalization of the anisotropic Hardy space of Bownik [12], the weighted anisotropic Hardy space of Bownik et al [16] as well as the Musielak-Orlicz Hardy space of Ky [60].…”