Equivalence of (quasi-)norms on a vector-valued function space and its applications to multilinear operators

Bae Jun Park

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arXiv · 1903.08892

Equivalence of (quasi-)norms on a vector-valued function space and its applications to multilinear operators

Bae Jun Park

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Abstract

In this paper we present (quasi-)norm equivalence on a vector-valued function space $L^p_A(l^q)$ and extend the equivalence to $p=\infty$ and $0<q<\infty$ in the scale of Triebel-Lizorkin space, motivated by Fraizer-Jawerth. By applying the results, we improve the multilinear Hormander's multiplier theorem of Tomita, that of Grafakos-Si, and the boundedness results for bilinear pseudo-differential operators, given by Koezuka-Tomita.

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Bae Jun Park. 2019-03-21. Equivalence of (quasi-)norms on a vector-valued function space and its applications to multilinear operators. https://arxiv.org/abs/1903.08892

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