Acta Mathematica Sinica-English Series最新文献_第5页

Musielak–Orlicz–Lorentz Hardy Spaces: Maximal Function, Finite Atomic, and Littlewood–Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms Musielak-Orlicz-Lorentz Hardy空间：极大函数、有限原子和Littlewood-Paley刻画及其在对偶空间和傅里叶变换可和性上的应用

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3153-2

Hongchao Jia, Der-Chen Chang, Ferenc Weisz, Dachun Yang, Wen Yuan

{"title":"Musielak–Orlicz–Lorentz Hardy Spaces: Maximal Function, Finite Atomic, and Littlewood–Paley Characterizations with Applications to Dual Spaces and Summability of Fourier Transforms","authors":"Hongchao Jia, Der-Chen Chang, Ferenc Weisz, Dachun Yang, Wen Yuan","doi":"10.1007/s10114-025-3153-2","DOIUrl":"10.1007/s10114-025-3153-2","url":null,"abstract":"<div>Let q ∈ (0, ∞] and φ be a Musielak–Orlicz function with uniformly lower type p\u0000 −φ\u0000 \u0000 ∈ (0, ∞) and uniformly upper type p\u0000 +φ\u0000 \u0000 ∈ (0, ∞). In this article, the authors establish various real-variable characterizations of the Musielak–Orlicz–Lorentz Hardy space Hφ,q(ℝn), respectively, in terms of various maximal functions, finite atoms, and various Littlewood–Paley functions. As applications, the authors obtain the dual space of Hφ,q(ℝn) and the summability of Fourier transforms from Hφ,q(ℝn) to the Musielak–Orlicz–Lorentz space Lφ,q(ℝn) when q ∈ (0, ∞) or from the Musielak–Orlicz Hardy space Hφ(ℝn) to Lφ,q(ℝn) in the critical case. These results are new when q ∈ (0, ∞) and also essentially improve the existing corresponding results (if any) in the case q = ∞ via removing the original assumption that φ is concave. To overcome the essential obstacles caused by both that φ may not be concave and that the boundedness of the powered Hardy–Littlewood maximal operator on associated spaces of Musielak–Orlicz spaces is still unknown, the authors make full use of the obtained atomic characterization of Hφ,q(ℝn), the corresponding results related to weighted Lebesgue spaces, and the subtle relation between Musielak–Orlicz spaces and weighted Lebesgue spaces.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"1 - 77"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Sense of Convergence in the Dyadic Representation Theorem 关于并矢表示定理的收敛意义

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3698-0

Tuomas Hytönen

引用次数: 0

Mapping Properties of Fourier Transforms, Revisited 傅里叶变换的映射性质

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3532-8

Dorothee D. Haroske, Leszek Skrzypczak, Hans Triebel

{"title":"Mapping Properties of Fourier Transforms, Revisited","authors":"Dorothee D. Haroske, Leszek Skrzypczak, Hans Triebel","doi":"10.1007/s10114-025-3532-8","DOIUrl":"10.1007/s10114-025-3532-8","url":null,"abstract":"<div>The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished Besov spaces B\u0000 sp\u0000 \u0000 (ℝn) = B\u0000 sp,p\u0000 \u0000 (ℝn), 1 ≤ p ≤ ∞, and between Sobolev spaces H\u0000 sp\u0000 \u0000 (ℝn), 1 < p < ∞. In contrast to the paper H. Triebel, Mapping properties of Fourier transforms. Z. Anal. Anwend. 41 (2022), 133–152, based mainly on embeddings between related weighted spaces, we rely on wavelet expansions, duality and interpolation of corresponding (unweighted) spaces, and (appropriately extended) Hausdorff-Young inequalities. The degree of compactness will be measured in terms of entropy numbers and approximation numbers, now using the symbiotic relationship to weighted spaces.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"231 - 254"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains 穿孔区域上退化椭圆方程的一致正则性

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3640-5

Zhongwei Shen, Jinping Zhuge

引用次数: 0

A Remark on Stein–Tomas Type Restriction Theorems 关于Stein-Tomas型约束定理的一个注解

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3525-7

Xiaochun Li

引用次数: 0

New Characterization of Morrey-Herz Spaces and Morrey-Herz-Hardy Spaces with Applications to Various Linear Operators Morrey-Herz空间和Morrey-Herz- hardy空间的新表征及其在各种线性算子上的应用

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3570-2

Kwok Pun Ho, Yoshihiro Sawano

引用次数: 0

Embeddings of Generalised Morrey Smoothness Spaces 广义Morrey平滑空间的嵌入

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3553-3

Dorothee D. Haroske, Zhen Liu, Susana D. Moura, Leszek Skrzypczak

{"title":"Embeddings of Generalised Morrey Smoothness Spaces","authors":"Dorothee D. Haroske, Zhen Liu, Susana D. Moura, Leszek Skrzypczak","doi":"10.1007/s10114-025-3553-3","DOIUrl":"10.1007/s10114-025-3553-3","url":null,"abstract":"<div>We study embeddings between generalised Triebel–Lizorkin–Morrey spaces (cal{E}_{varphi,p,q}^{s}(mathbb{R}^{d})) and within the scales of further generalised Morrey smoothness spaces like (cal{N}_{varphi,p,q}^{s}(mathbb{R}^{d})), B\u0000 s,φp,q\u0000 \u0000 (ℝd) and F\u0000 s,φp,q\u0000 \u0000 (ℝd). The latter have been investigated in a recent paper by the first two authors (2023), while the embeddings of the scale (cal{N}_{varphi,p,q}^{s}(mathbb{R}^{d})) were mainly obtained in a paper of the first and last two authors (2022). Now we concentrate on the characterisation of the spaces (cal{E}_{varphi,p,q}^{s}(mathbb{R}^{d})). Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’ wavelets. Then we prove necessary and sufficient conditions for the embedding (cal{E}_{varphi_{1},p_{1},q_{1}}^{s_{1}}(mathbb{R}^{d})hookrightarrowcal{E}_{varphi_{2},p_{2},q_{2}}^{s_{2}}(mathbb{R}^{d})). We can also provide some almost final answer to the question when (cal{E}_{varphi,p,q}^{s}(mathbb{R}^{d})) is embedded into C(ℝd), complementing our recent findings in case of (cal{N}_{varphi,p,q}^{s}(mathbb{R}^{d})).</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"413 - 456"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Weighted Estimates for Generalised Conical Square Functions and Applications 广义圆锥平方函数的加权估计及其应用

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3478-x

The Anh Bui, Xuan Thinh Duong, Ji Li

引用次数: 0

Conformal Composition for Borderline Fractional Sobolev Spaces 边界分数Sobolev空间的保角复合

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3649-9

Nijjwal Karak, Pekka Koskela, Debanjan Nandi, Swadesh Kumar Sahoo

引用次数: 0

Bilinear Exotic Calderón-Zygmund Operators 双线性奇异Calderón-Zygmund算子