{"title":"变指数的变各向异性Hardy空间","authors":"Zhenzhen Yang, Yajuan Yang, Jiawei Sun, Baode Li","doi":"10.1515/agms-2020-0124","DOIUrl":null,"url":null,"abstract":"Abstract Let p(·) : ℝn → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝn introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp(·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp(Θ) on ℝn with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp(·)(Θ) to Lp(·)(ℝn) in general and from Hp(·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp(Θ).","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":"9 1","pages":"65 - 89"},"PeriodicalIF":0.9000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2020-0124","citationCount":"2","resultStr":"{\"title\":\"Variable Anisotropic Hardy Spaces with Variable Exponents\",\"authors\":\"Zhenzhen Yang, Yajuan Yang, Jiawei Sun, Baode Li\",\"doi\":\"10.1515/agms-2020-0124\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let p(·) : ℝn → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝn introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp(·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp(Θ) on ℝn with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp(·)(Θ) to Lp(·)(ℝn) in general and from Hp(·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp(Θ).\",\"PeriodicalId\":48637,\"journal\":{\"name\":\"Analysis and Geometry in Metric Spaces\",\"volume\":\"9 1\",\"pages\":\"65 - 89\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/agms-2020-0124\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Geometry in Metric Spaces\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/agms-2020-0124\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Geometry in Metric Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/agms-2020-0124","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Variable Anisotropic Hardy Spaces with Variable Exponents
Abstract Let p(·) : ℝn → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝn introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp(·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp(Θ) on ℝn with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp(·)(Θ) to Lp(·)(ℝn) in general and from Hp(·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp(Θ).
期刊介绍:
Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed.
AGMS is devoted to the publication of results on these and related topics:
Geometric inequalities in metric spaces,
Geometric measure theory and variational problems in metric spaces,
Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density,
Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds.
Geometric control theory,
Curvature in metric and length spaces,
Geometric group theory,
Harmonic Analysis. Potential theory,
Mass transportation problems,
Quasiconformal and quasiregular mappings. Quasiconformal geometry,
PDEs associated to analytic and geometric problems in metric spaces.