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Mixed multiplication of Besov and Triebel-Lizorkin spaces (2301.03259v1)
Published 9 Jan 2023 in math.FA
Abstract: This paper is concerned with proving some embeddings of the form \begin{equation*} F_{p_{1},q}{s_{1}}\cdot B_{p_{2},\infty }{s_{2}}\cdot...\cdot B_{p_{m},\infty }{s_{m}}\hookrightarrow F_{p,q}{s_{1}},\quad m\geq 2. \end{equation*} The different embeddings obtained here are under certain restrictions on the parameters. In particular, we improve some results of pointwise multiplication on Triebel-Lizorkin spaces. Franke-Jawerth embeddings, the $\pm $ - method of Gustaffson-Peetre and the relation between Hardy spaces and Triebel-Lizorkin spaces are the main tools.