Littlewood - Paley theorem on $L^{p(t)}(\mathbb{R}^n)$ spaces

• Date: 2008
• Main Authors: Kopaliani, T. S., Копаліані, Т. С.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3283
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We point out that when the Hardy - Littlewood maximal operator is bounded on the space $L^{p(t)}(\mathbb{R}^n),\quad 1 < a \leq p(t) \leq b < \infty,\quad t \in \mathbb{R}$, the well-known characterization of spaces $L^{p(t)}(\mathbb{R}^n),\quad 1 < p < \infty$, by the L...