Abstract
First, we define \( \left\| \cdot \right\|_{\Lambda _a } \) and \( \left\| \cdot \right\|_{H^p } \) HP for Rm-valued functions \( \vec f\left( x \right) = \left( {f_1 \left( x \right), \cdots ,f_m \left( x \right)} \right) \) defined on R n by exactly the same way as in Sections 1 and 2. In the following, \( \left| {\vec f\left( x \right)} \right| \) \( \left\{ {\sum\limits_{j = 1}^n {\left| {f_j \left( x \right)^2 } \right|} } \right\}^{1/2} \).
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© 2001 Springer Japan
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Uchiyama, A. (2001). Preliminaries for characterizations of H p in terms of Fourier multipliers. In: Hardy Spaces on the Euclidean Space. Springer Monographs in Mathematics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-67905-9_17
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DOI: https://doi.org/10.1007/978-4-431-67905-9_17
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-67999-8
Online ISBN: 978-4-431-67905-9
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