Weak Triebel–Lizorkin Spaces with Variable Integrability, Summability and Smoothness

Weak Triebel–Lizorkin spaces with variable integrability, summability and smoothness are first introduced. Then we establish a vector estimate for weak Lebesgue spaces with variable exponent. As an application we give equivalent quasi-norms in these new spaces by means of Peetre's maximal funct...

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Bibliographic Details
Published inPublications of the Research Institute for Mathematical Sciences Vol. 55; no. 2; pp. 259 - 282
Main Authors Li, Wenchang, Xu, Jingshi
Format Journal Article
LanguageEnglish
Published Zuerich, Switzerland European Mathematical Society Publishing House 01.01.2019
Subjects
Differential equations
Fourier analysis
Functional analysis
Triebel–Lizorkin space
maximal function
molecule
weak Lebesgue space
atom
Variable exponent
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ISSN0034-5318
1663-4926
DOI10.4171/PRIMS/55-2-2

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Summary:Weak Triebel–Lizorkin spaces with variable integrability, summability and smoothness are first introduced. Then we establish a vector estimate for weak Lebesgue spaces with variable exponent. As an application we give equivalent quasi-norms in these new spaces by means of Peetre's maximal functions. Finally, we obtain the boundedness of the $\varphi$ transform on these new spaces and their atomic and molecular decompositions.
ISSN:0034-5318
1663-4926
DOI:10.4171/PRIMS/55-2-2