FRANKE-JAWERTH EMBEDDINGS FOR BESOV AND TRIEBEL-LIZORKIN SPACES WITH VARIABLE EXPONENTS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390880" target="_blank" >RIV/00216208:11320/18:10390880 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.5186/aasfm.2018.4310" target="_blank" >https://doi.org/10.5186/aasfm.2018.4310</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5186/aasfm.2018.4310" target="_blank" >10.5186/aasfm.2018.4310</a>
Alternative languages
Result language
angličtina
Original language name
FRANKE-JAWERTH EMBEDDINGS FOR BESOV AND TRIEBEL-LIZORKIN SPACES WITH VARIABLE EXPONENTS
Original language description
The classical Jawerth and Franke embeddings F-p0,q(s0)(R-n) hooked right arrow B-p1,p0(s1)(R-n) and B-p0,p1(s0)(R-n) hooked right arrow F-p1,q1(s1)(R-n) are versions of Sobolev embedding between the scales of Besov and Triebel-Lizorkin function spaces for s(0) > s(1) and s(0) - n/p(0) = s(1) - n/p(1). We prove Jawerth and Franke embeddings for the scales of Besov and Triebel-Lizorkin spaces with all exponents variable F-p0(.),q(.)(s0(.))(R-n) hooked right arrow B-p1(.),p0(.)(s1(.))(R-n) and B-p0(.),q(.)(s0(.))(R-n) hooked right arrow F-p1(.),p0(.)(s1(.))(R-n), respectively, if inf(x is an element of Rn)(s(0)(x) - s(1)(x)) > 0 and s(0)(x) = n/P-0(x) = s(1)(x) - n/p(1)(x), x is an element of R-n. We work exclusively with the associated sequence spaces b(P(.),q(.))(s(.))(R-n) and f(P(.),q(.))(s(.))(R-n), which is justified by well known decomposition techniques. We give also a different proof of the Franke embedding in the constant exponent case which avoids duality arguments and interpolation. Our results hold also for 2-microlocal function spaces B-P(.),q(.)(omega)(R-n) and F-P(.),q(.)(omega)(R-n) which unify the smoothness scales of spaces of variable smoothness and generalized smoothness spaces.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annales Academiae Scientiarum Fennicae - Mathematica
ISSN
1239-629X
e-ISSN
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Volume of the periodical
43
Issue of the periodical within the volume
1
Country of publishing house
FI - FINLAND
Number of pages
23
Pages from-to
187-209
UT code for WoS article
000429434500009
EID of the result in the Scopus database
2-s2.0-85042879987