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On Hardy‐Bessel Potential Spaces Over the 2‐Series Field
Author(s) -
Tateoka Jun
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941680117
Subject(s) - mathematics , bessel function , hardy space , pure mathematics , fourier series , equivalence (formal languages) , mathematical analysis , field (mathematics) , series (stratigraphy) , paleontology , biology
The purpose of this paper is to present characterizations of the inhomogeneous Hardy‐Bessel potential spaces F p α ( K ) over the 2‐series field K defined by Littlewood‐Paley type function,where Δ 0 ( x ) = 1(|x|≥1), = 0(other), Δ j ( x ) = 2 j ≥, = 0(other) ( j ≥ 1). These characterizations are given by difference of functions, ball means of difference and atoms. As applications of these results we shall determine when F p α ( K ) is a multiplication algebra, and prove the lower majorant property, the uniform localization property and the equivalence of Fourier multipliers.