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Characterization of Triebel–Lizorkin type spaces with variable exponents via maximal functions, local means and non‐smooth atomic decompositions
Author(s) -
Gonçalves Helena F.,
Moura Susana D.
Publication year - 2018
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.201700257
Subject(s) - mathematics , pointwise , multiplier (economics) , pure mathematics , type (biology) , birnbaum–orlicz space , characterization (materials science) , cover (algebra) , maximal function , mathematical analysis , interpolation space , functional analysis , ecology , materials science , biology , nanotechnology , mechanical engineering , biochemistry , chemistry , engineering , gene , economics , macroeconomics
In this paper we study the maximal function and local means characterizations and the non‐smooth atomic decomposition of the Triebel–Lizorkin type spaces with variable exponentsF p ( · ) , q ( · )s ( · ) , ϕ( R n ) . These spaces were recently introduced by Yang et al. and cover the Triebel–Lizorkin spaces with variable exponentsF p ( · ) , q ( · ) s ( · )( R n )as well as the classical Triebel–Lizorkin spacesF p , q s ( R n ) , even the case when p = ∞ . Moreover, covered by this scale are also the Triebel–Lizorkin‐type spacesF p , q s , τ( R n )with constant exponents which, in turn cover the Triebel–Lizorkin–Morrey spaces. As an application we obtain a pointwise multiplier assertion for those spaces.