大贝索夫-布尔干姆雷空间及其在算子有界性中的应用

IF 1.4 3区 数学 Q1 MATHEMATICS
Yijin Zhang, Dachun Yang, Yirui Zhao
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引用次数: 0

摘要

Let\(1<qle p\le rle\le \infty \) and\(\tau \in (0,\infty ]\).Besov-Bourgain-Morrey空间({\mathcal {M}}\dot{B}^{p,\tau }_{q,r}({\mathbb {R}}^n)\ )在\(\tau =r\)的特殊情况下,扩展了J. Bourgain引入的内容,在与Strichartz估计和非线性薛定谔方程有关的研究中被证明是有用的。在这篇文章中,作者巧妙地混合了大勒贝格空间和贝索夫-布尔甘-莫雷空间的规范结构,并添加了一个额外的指数 \(\theta \in [0,\infty )\)、作者引入了一类新的函数空间,称为广义大贝索夫-布尔干姆雷空间({\mathcal {M}}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\).作者探讨了它们的各种实变性质,包括前二元空间、Gagliardo-Peetre 和 ± 插值定理。通过建立与 Muckenhoupt \(A_1({\mathbb {R}}^n)\weights 相关的 \({\mathcal {M}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\ 的一些等价准矩阵、作者随后得到了一个外推法定理({\mathcal {M}}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\ )。作者应用这一外推法定理、卡尔德龙积以及 \({\mathbb {R}}^n\) 的稀疏二元网格族,建立了 \({\mathcal {M}}\dot{B}^{p、\tau }_{q),r,\theta }({\mathbb{R}}^n)\)上的哈代-利特尔伍德最大算子、分数积分和卡尔德龙-齐格蒙算子的尖锐有界性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Grand Besov–Bourgain–Morrey spaces and their applications to boundedness of operators

Let \(1<q\le p \le r\le \infty \) and \(\tau \in (0,\infty ]\). Besov–Bourgain–Morrey spaces \({\mathcal {M}}\dot{B}^{p,\tau }_{q,r}({\mathbb {R}}^n)\) in the special case where \(\tau =r\), extending what was introduced by J. Bourgain, have proved useful in the study related to the Strichartz estimate and the non-linear Schrödinger equation. In this article, by cleverly mixing the norm structures of grand Lebesgue spaces and Besov–Bourgain–Morrey spaces and adding an extra exponent \(\theta \in [0,\infty )\), the authors introduce a new class of function spaces, called generalized grand Besov–Bourgain–Morrey spaces \({\mathcal {M}}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\). The authors explore their various real-variable properties including pre-dual spaces and the Gagliardo–Peetre and the ± interpolation theorems. Via establishing some equivalent quasi-norms of \({\mathcal {M}}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\) related to Muckenhoupt \(A_1({\mathbb {R}}^n)\)-weights, the authors then obtain an extrapolation theorem of \({\mathcal {M}}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\). Applying this extrapolation theorem, the Calderón product, and the sparse family of dyadic grids of \({\mathbb {R}}^n\), the authors establish the sharp boundedness on \({\mathcal {M}}\dot{B}^{p,\tau }_{q),r,\theta }({\mathbb {R}}^n)\) of the Hardy–Littlewood maximal operator, the fractional integral, and the Calderón–Zygmund operator.

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来源期刊
Analysis and Mathematical Physics
Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.70
自引率
0.00%
发文量
122
期刊介绍: Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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