本征平方函数在变指数极大 Herz-Morrey空间的有界性

Boundedness of Intrinsic Square Function on Variable Grand Herz-Morrey Space

摘要

利用变指数函数空间理论和函数分层分解等方法,证明本征平方函数在变指数极大 Herz-Morrey空间$M \dot{K}_{\lambda, q(\cdot)}^{\alpha(\cdot), p, \theta}\left(\mathbb{R}^{n}\right)$中的有界性,其中α(·)和q(·)均为变指数.

Abstract

By using methods such as the theory of variable exponent function spaces and hierarchical decomposition of function, we prove the boundedness of the intrinsic square function on variable grand Herz-Morrey space $M \dot{K}_{\lambda, q(\cdot)}^{\alpha(\cdot), p, \theta}\left(\mathbb{R}^{n}\right) $, where α(·) and q(·) are both variable exponents.

关键词

本征平方函数 / 变指数极大 Herz-Morrey空间 / $\mathscr{P}_{\infty}^{\log }\left(\mathbb{R}^{n}\right) $条件 / 有界性

Key words

intrinsic square function / variable grand Herz-Morrey space / $\mathscr{P}_{\infty}^{\log }\left(\mathbb{R}^{n}\right) $ condition / boundedness

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基金资助

国家自然科学基金(12361018)